If you have any tips to share it would be much appreciated. i'd have a closer look during the weekend... in the meantime: is it dangerous to operate the scope in this state?
OK. The EHT cap on the CRT will be a big rubber or silicone disk on the side of the tube, like a suction cap with the thick-insulation EHT wire coming out of it. Inside in the center it has a metal thing that clips into the EHT button set in the glass. The button is usually a cylindrical hole with an inwards-facing flange level with the glass surface.
The disk connector can be either a kind of snap-in spring (that can be pulled off) or more usually a metal U-shaped spring with outward hooks on the ends of the U. These grip under that flange, so these type do NOT just pull off.
The CRT anode consists of a conductive layer deposited on the inside of the glass over most of the fat end of the tube. With the grounded conductive paint (black stuff) on the outside of the tube, this makes a big capacitor. Which is what you have to discharge to be safe to work on. You have to short the inside of the tube (via the EHT connector) to the outside of the tube. Which will always be electrically connected to the instrument chassis.
How to discharge it: Screwdriver with a thin, longish shaft (flat head best) and a very well insulated handle, plus a fairly short and solid alligator clip lead. Clip one alligator to the screwdriver shaft, the other end to the closest metal part that is *definitely* well attached to the conductive outside of the CRT. On TVs this is obvious - the wire braid straps held by springs to the outside of the tube. On scopes it's sometimes a bit less obvious.
Anyway, once you are sure the screwdriver can't become +20KV hot relative to anything, slide the blade end in under the EHT cap, towards the center contact. If there's any charge in the CRT you'll hear a SNAP as it arcs to the screwdriver before it even touches the contact. Not to worry, it's normal.
But don't stop there. Keep pushing it in till it definitely touches the center contact metal. Then leave it there, at least 15 seconds. Because there can be charge on various internals of the tube, that can leak gradually back to the EHT conductive lining so even if you briefly shorted the EHT contact, it can become somewhat charged again later.
Once you are really sure all the charge is gone (paranoia is appropriate) then you can pull the EHT cap off the tube.
If it doesn't come off with a firm pull (like a pop-stud) then it's probably the hooks type. For these, try pushing the cap center inwards plus sideways, to get one side of the 'U' to unhook. Sometimes you can peel the rubber disk edge up enough to see it to figure out how to release it. Or try feeling for the clip with the screwdriver. Just never, ever poke anything conductive under that cap unless it's firmly wired to the case ground.
With some scopes the rubber EHT cap is glued onto the CRT. Leave those alone; there will be a connector of some kind in the EHT cable. Same routine - you have to get at the conductor with a grounded lead. Don't do what I did with one scope, which was unplug that connector (intending to short the pin to chassis) but then fumble the connector so it dropped past a PCB. That scope (a Tek 7104) is still dead.
Oh, one other caution. The metal contact sealed in the CRT glass has a thin bottom end, with vacuum on the other side. Don't be poking it with pointy objects. (Though it's fun to do deliberately with big old TV CRTs, as one way to make them safe for disposal.)
As for 'safe to operate like that' - depends what you mean by safe, and where the arc is occurring. If you mean safe for you, sure. Safe for the equipment - if the arc is in dust on the CRT glass, no problem. If it's along a surface that can burn and carbonize, forming permanent conductive tracks, then no.