Don't run the PSU with the cover removed, not even for a brief test, because having the cover screwed in place will protect against exploding capacitors and electric shock.
When replacing any high voltage transistor, be sure to electrically insulate it properly. Some transistor packages require an insulating sheet (silicone rubber, mica, kapton plastic) and a nylon shoulder washer (not regular washer), while others don't need the washer or sheet. Also for any transistor with a given part number, the maximum power rating can differ by 3:1 because of the package type. If you need to apply thermal paste between the transistor and heatsink, use transistor heatsink grease or dielectric grease from an electronic parts supply (even Radio Shack) or an auto parts store, not anything containing pure metal, like Arctic Silver, which conducts electricity and may be unsafe for high voltage (Arctic Silver doesn't know the maximum safe voltage and is snotty about this matter, yet they brag that it's used on high voltage transistors for windmills). BTW you can't reliably test any grease for electrical conduction with just an ohm meter because even stuff loaded with pure metal powder will measure as an insulator.
I've found the easiest way to remove a big transistor or diode in a tightly packed PSU is to unsolder everything on its heatsink and pull out the whole heatsink.