Bathtub it bro. The 1080 has that big torroidal transformer which is relatively protected and nothing else to really worry about. I'd easily give one of those a light wash without disassembly if it was just a basic dust-and-cat-hair situation.
Now I do NOT mean submerse it, which is where you'd get into trouble, but what I'd do is (after pulling the knobs & front panel) put it in sink/tub (I use a rubbermaid dish tray underneath to protect both unit and porcelain), get some hot soapy water and a medium soft paint brush. first just wet it down from the top, then go around scrubbing with the paint brush and soapy water. if you get the right bristle stiffness it will scrub muck away pretty well without being able to push components around (you obv don't want to make something short out because you bent the leads over). then douche liberally with clean water for a rinse.
Now this is relatively safe but I still try to do it quickly to minimize any soaking-into-crevices and joints that might happen. For a basic unit I'm usually done in 2-3 minutes.
Also be very careful around the tuner bits. If you bend or tweak the variable capacitor fins at all your whole tuner will be outa whack and need a realignment. Same for my comments about inductors above.
After that, I have the benefit of giant cast iron radiators in my place, so I'll put the bare unit (still with front panel / knobs / case off) right on one of those that doesn't get too hot, with a fan across it for hours. It's be a nice super-low-temperature bake to dry everything right out.
Once that first wash is done depending on the unit I might have to go back with solvents for spot cleaning. Or if there's still some water spots left, a rag with some alcohol or windex on flat surfaces (think outsides of big filter capacitors, tops of transformers, etc.)
I'm looking for a quick bit of re-assurance on something. I recently cleaned an old Pioneer SX-1000TA using a half bottle of Windex, and it seems to have done a pretty good job. I let it dry for a week before I plugged it back in. The FM section is still out, but everything that worked before worked after.
I'm looking to do the same with my Pioneer SX-1080. I've read many posts that discourage getting the tranformer and related bits soaked. I plan on taking a damp cloth to those parts, and protecting them with cardboard or other material while I bathe the rest of the unit. I should be in the clear, right? I wouldn't mind taking the whole thing apart except I don't have any of the gear to put it back together (soldering iron, etc). I really just want to wash away a lot of the dust and gunk. Funny how you just set out to tidy up the pots and take care of the static, and end up doing much more.