I've cleaned plenty of plywood cabs by spraying with your favorite cleaner (Formula 409, Greased Lightning, Simple Green, etc), then wiping down with a damp facecloth or terry rag. Repeat a few times if necessary. (Also, vacuum out the cab thoroughly first, to get most of the big junk out.) I've done all of my Atari cabs this way, and they've come out clean enough to eat off of, as long as they're not soaked with rat piss, etc.
You want to be careful if it's particleboard, as getting that wet with pretty much anything can cause it to start to swell and crumble. But for plywood bottoms of cabs, etc (or if it's laminated or painted), you can get it damp briefly fairly safely. Not soaked though. I'll use a fan to dry it out quickly also, as you don't want to let it sit soaking wet for a long time, if you can avoid it.