Overriding most other concerns, if it ain't broke....
Secondly, until it is profoundly gross, dirt and grime doesn't affect anything unless you believe that it will attract conductive dust. If wax has dripped onto the chassis, that is possibly leaked wax from old caps or filter caps. Again, unless you think it will attract conductive dust, it just doesn't affect anything. I know it probably bothers you but it doesn't really affect anything. Maybe you can scrape/scoop some away with a popsicle stick or some Q-tips. Inside the amp you might try some rubbing alcohol, prefer the 91% variety to the 70% variety, but that rarely does a very good job, meaning you do the work and it still isn't clean-clean.
You can try windex or some alcohol on the panel but you really don't want to wear away any of the silkscreened paint and that's unfortunately easy to do. And it's easy to get alcohol from whatever you do on the inside to drip onto the outside which risks dissolving the silkscreen.
Most often the best course is really to do nothing. If you show me your '53 Chevy and there are brand new rubber brake pedal and clutch pads, I am happy to have the new brake pads, but on further thought it leads me to believe you have ridden the clutch or jammed your foot onto the brakes so much you wore out the rubber pad, and now I worry about the clutch and the brakes. The truth is that you are more likely to break something or create something in the appearance that looks odd. Or produce a funny stain on the covering. My advice: Button it up and enjoy it the way it is. If the chassis gets hot...6BQ5s *do* run hot in most cases, and Gibson sometimes used somewhat undersized transformers which can heat up. If you're worried about heat, more productive than chemical or mechanical "cleanup" that risks some esthetic damage would be to figure out a way to mount a little fan in the back, some kind of WalMart $7 special, hopefully with a spring clip that requires no drilling or screws into the wood of the cabinet.
If you've seen a lot of old amps, you've seen a lot of weird stuff that people did who thought they were being clever.