Hi nibo,
Sounds like an interesting project- I am a bit of a scope addict and have messed with all kinds of scopes over the years. What model scope do you have? Any chance of a picture?
You are wise to be cautious, but you seem to have been exposed to some pretty exaggerated warnings.
The first thing, whatever you are doing, is to wear safety glasses- your eyes are easily damaged. I even wear safety glasses while mowing the lawn. The next general precaution is never put your face near to batteries, electrolytic capacitors and the like- just like you would never look down the barrel of a gun.
At last to the scope:
You will need a stiff, medium-sized art brush, a small container (soup bowl if the wife isn't looking
), and a bottle of 95%, or purer, isopropyl alcohol (IPA).
With a dry brush clean all surface dust away, especially in any nooks and crannies. A vacuum cleaner nozzle may also be used. While you are cleaning make sure you do not disturb any components. You can also blow the dust out if you wish but go easy with the pressure.
There are two areas that require special cleaning and inspection, especially on a scope as old as yours: CRT, HT/EHT power supply. Over the years both areas tend to become greasy and the grease absorbs dust. The end result is that you get an unpleasant foul-smelling deposit which can be conductive and affect the operation of both areas.
The CRT will be mounted in a mumetal screen which covers the whole CRT, except the viewing screen and the pins at the rear that connect to a valve holder. At the front on the neck, the mumetal screen will also have an aperture for the EHT connector, which fits into a well in the glass.
There are two types of EHT connector: push fit, wire spring. The push fit type simply pulls out, but be very careful. With the spring type, squeeze the rubber boot of the connector so that the spring clip under the rubber boot is compressed. This will allow the connector to be lifted out of the well in the CRT neck. Be careful and do not use much force. The connector will pull out of the glass well quite easily if you have compressed the spring correctly. Some times the EHT connector gets stuck in the well and the boot gets stuck to the CRT neck. If this is the case apply some IPA to the area and gently push/rock the connector until it frees. Be careful though.
Next, go to the tail of the CRT and gently pull off the valve holder.
Clean all the areas of the CRT now exposed with the brush dipped in IPA. Pay particular attention to the area of the CRT where the EHT connector well is. Do not fill the well with IPA.
Keep cleaning until every thing is squeaky clean. Do the same with the EHT connector and its rubber boot. Also clean the EHT lead in the same way. Inspect the EHT lead for cracks and if there are any insulating stand-off washers on the EHT lead also inspect them. In general, the EHT lead should be routed so that it does not get close to other parts of the scope. Stand-off insulating washers are sometimes used for this purpose.
With fine wet and dry sandpaper (not woodworking sandpaper) lightly burnish the pins on the CRT base, ensuring not to use excessive force. With a fine round needle file, or better still welding pipe nozzle cleaner (cheap on ebay), lightly burnish the sockets in the valve holder. You will probably find that the two heater pins will be heavily tarnished, so pay particular attention to them. Finally, clean the valve holder and all its components with IPA.
The valve holder may have a PCB connected directly to it. If this is the case, inspect all components, the PCB traces, and the solder joints, which crystallize with heat and age. This is a common fault, especially the two CRT heater joints.
Give the HT/EHT PSU a similar treatment, especially checking for PCB trace cracks and crystallized joints. If the EHT PSU uses valves, burnish the valve pins and valve base sockets, as previously described. If the HT/EHT PSU uses transistors, pay particular attention to the power transistor that drives the EHT transformer. It is best to remove the power transistor and give it a good clean. Also give the mating surface of the heatsink a good clean. Then, using good thermal grease and a new mica washer (not plastic or foam), remount the power transistor using new insulating washers on the bolt(s). You do all this because often, with time and heat, the thermal grease hardens and cracks, which results in poor heat conduction. The power transistor then runs very hot and the thermal stress can cause poor performance or even complete failure.
Now to the difficult part: the EHT transformer. EHT transformers are very delicate and have fine wires which easily break. But it is essential that the windings and flying leads, if present, are cleaned so be very careful. Hopefully your EHT transformer will not have flying leads.
Unless you have a high end scope: Tektronix, hp etc, the EHT PSU is likely to be badly designed. Very often the high voltage terminals are so close to the EHT PSU metalwork that they ark, especially if the metal work is bent or misaligned. So check this and if it appears to be a problem modify the EHT PSU to eliminate the problem.
In general be suspicious of any areas the involve high voltage/high power. This includes the x and y amplifier output transistors, which may need the same treatment as the HT/EHT transformer driver transistor.
WARNING
Before you use IPA on any parts check in a small area that the IPA does not dissolve any plastic/wax and that it does not remove any legend. I have never had a problem with scopes, but some computer parts are not compatible with IPA.
UPDATE (2018_11_20) Best not to use IPA on the outside of the scope, including knobs (thanks to TERRAoperative: reply#7)
And that is it- good luck