I would not float the soldering iron tip. Any bad connection or loose wire would cause a big problem. Just keep DC(-) and the tip and enclosure grounded together to PE, like soldering stations have been doing for many decades.
I don't suggest daisy-chaining the ground for the ESD mat and wrist-strap.
That way, one open connection at the mains PE wire would make the mat, wristband and soldering iron all float up together.
In production environments, after years the wires get broken or screws loose and it is possible to have a bad ground.
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Yeah, I know, but what'yer gonna do about it?
I started reading this thread after following a link from the "Cheap T12 clone soldering stations" thread I'd stumbled upon in my search for a T12-9501 soldering handle wiring diagram to positively confirm which way round to best wire in the ball bearing shake sensor switch.
I'd already made a diagram from two months back when I'd rewired the supplied handle of a KSGER T12 soldering station with oled display (proper aluminium cased version) but hadn't noted that this switch actually had a 'polarity' (I hadn't actually had to remove it from the earth tag in the handle so had missed this little fact of its construction).
I did finally come across a posted diagram in that other thread and duly voted a 'thank you' to Zanga for his Reply #148 on: September 18, 2018
https://www.eevblog.com/forum/reviews/cheap-t12-clone-soldering-stations/msg1832351/#msg1832351.
In hindsight, I suppose I could have worked it out for myself with a continuity test as I did once I'd confirmed that the 'gold' wire end is meant to connect to that tag and the blue wire to the 'silver' wire end (in case anyone's curious - the glass thermistor, btw, can go either way round). Basically, you want the ball resting against the disk contact (gold wire end) so that it makes an intermittent contact to the cup contact whilst soldering (ie the gold end pointing down). If you fit it the other way round, you'll land up having to rely on allowing the station's buzzer to remind you to tilt it up on every time out to reset whatever time out period you had chosen. Anyway, I digress...
What caught my attention here was this issue of "Touch Voltage" which virtually all small to medium power smpsus are afflicted with. Firstly (at least in the EU) we can blame the EMC directive in mandating the use of the dreaded Y cap measure to mitigate conducted common mode interference along the low voltage dc cable as a result of coupling via the high frequency isolation/stepdown transformer's inter-winding capacitance from the 150 or (in my case) 300 volt high frequency spikes produced by the HT switching of the 170 or (again in my case) 350 volts dc produced by directly rectifying the incoming mains and smoothing it (fvsvo 'smoothing') with a BFO 400 or 450 VDC rated cap to the tune of ~1μF per watt's worth of power rating (universal 90 to 265 vac mains voltage rating case), the idea being (like Brexiteer's demands on immigration) to send these unwanted voltage spikes back to where they had originated.
It works to a limited extent, perhaps by as much as 20dB's worth of attenuation if you're very lucky. It's less of the Aldididdle's "Once it's Gone, it's gone" slogan so much as Asda's "Every Little Helps." sort of a measure. However, this "20dB if you're lucky" prize does come with an unfortunate side effect, "Touch voltage" tingle (the classic 50 to 90 vac high impedance voltage seen with a typical DMM - it's actually half whatever the mains voltage supply happens to be, your 10MR DMM just loads the 1M6R typical of a 10W rated wallwart leakage voltage down to the 50 or 90 volt reading typically observed).
This is commonly seen in the case of class II wallwarts and cheap laptop charging bricks which forego the sheer unadulterated luxury of a PE connection. It's worth noting that even when an earthed laptop charging brick is plugged into an earthed outlet, it may still have this half live voltage if they've neglected to either connect the barrel (normally negative of the 19vdc output) to the PE or at least linked it to the PE via a 3 to 10KR 'bleed resistor' to bog down this leakage voltage to just a volt or less.
Incredibly, these aluminium cased oled KSGER stations aren't earthed despite the iron tips being connected to the PE tag of the C14 mains socket. Of course, mine is now well and truly earthed, but only
after I'd modified the BFO diode heatsink which bridges the HV/LV isolation slot to stop it resting on the solder resist mask which had been its only form of insulation from a circuit trace carrying the 350VDC from the BFO 68μF 400VDC rated smoothing cap!!!
TBH, I never tested to see whether this half live voltage was present on the DC output. The accursed Y cap which is typically wired in parallel with (often alongside of) the opto-isolator that provides the required voltage negative feedback to stabilise the voltage is still present in this smpsu board's circuitry. I can only conclude that it must have suffered this detriment but since I've linked the negative rail to the case and PE, I don't really care any more - it's not a signal generator where such a direct link between the BNC shields and mains earth is
not a good idea[1].
In theory, as long as the tip itself remains connected to the PE, it shouldn't matter whether or not the DC supply is floating at half mains live voltage. However, as most of us know full well, theory and practice are often at odds with each other and in this case, prudence suggests that it would be a most excellent idea to also independently ground the DC output (negative common rail point) so theory and practice are in full agreement (even if it's merely a 10KR to reduce this leakage voltage to just a volt or so - in this case, it not being a signal generator, a full zero ohms connection to the PE is the best and cheapest choice).
The OP's problem here appears to stem from the use of a mini station being powered off a laptop supply that suffers from this half mains live voltage issue. A simple test to verify that this voltage is merely the usual half mA or less from a 4n7F (max - it's more typically a 1nF cap) Y class EMC RFI suppression cap (typically 80μA in the case of the 1nF used in a 10W rated wallwart), would be to wire a 10KR resistor across the DMM voltage input terminals to verify that the voltage drops to around the 2 volts or less mark (and
doesn't blow the resistor to kingdom come!
).
Once this leakage voltage has been proved to be the normal condition (as opposed to a nasty fault condition - Y caps are designed to failsafe, ie
never ever go short but only open circuit), the common negative terminal can be tied to the PE connection alongside of the tip's ground connection to eliminate the risk of ESD damage to sensitive components.
[1] This reference to signal generators stems from the troublesome effects of ground loops you can let yourself in for if you do what Feeltech so foolishly did in response to customer moans about this half live mains touch voltage issue through the use of a non earthed (IEC C8 two wire mains cord socket) class II 10W rated smpsu board in the FY6600 model when they evolved it into the FY6800 model with its "Tail Wags Dog" BFO C14 mains socket on a 700 gram plastic boxed cheap arbitrary wave/function signal generator and hard wired the chassis ground to the PE by stealing one of the two ground wires in the ribbon cable, which links the smpsu board's +5 and +/-12 volt rails to the main board, as a ready to hand length of wire to solder directly onto the C14's PE tag.
IDIOTS! feckin utter
IDIOTS for perpetrating such
IDIOCITY 
My solution to the original problem with the earlier FY6600 model had been to completely give up the notion that I could find a two wire mains lead based solution and, by way of a compromise re the tail wags dog effect, fit an IEC C6 (trefoil or clover leaf) three pole mains socket to provide access to the PE by which to link the chassis ground via a 10KR "drain" resistor to squash the 90 odd volts down to a mere half volt ac of leakage.
The class II smpsu used in these signal generators doesn't actually require a hard connection to the PE which was only needed in this case as a means of killing the nasty touch voltage stone dead with a 3 to 10KR "drain" resistor which attenuates any unwanted signal/noise flows to and from the mains earth by some 50 to 60dB (including any undesired galvanic voltages and mains frequency interference from volt drops in the neutral wire due to running heavy domestic loads).
JBG
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