Re badness of solvents: they're all bad in different ways.
Organo-halides like perchloroethylene, triclhloroethylene, and the infamous carbon tetrachloride are all pretty bad news for your liver. I hurt myself with TCE and no gloves back when I was young and foolish. My liver enzymes eventually went back up to normal levels (I was in a job that included a full tox panel every six months), but it took about five years after a summer of exposure to the stuff. Now I'm quite careful not to get any of that class of solvent on my skin - it goes through it quite well. Neoprene gloves are quite helpful for this sort of thing. There's also an inhalation risk, of course, but if you have any sense, you use it outdoors, so contact is the more dangerous problem. In the longer run, several of these compounds are known carcinogens, so limit total exposure, and give your body a rest of a week or more between exposures if you get a hole in a glove or something like that.
On the other side of the ring we have aromatic hydrocarbons. Benzene, toluene, xylene, and naptha (which is a distillate soup) are typical. Many of these are carcinogens as well (particularly benzene and naphthalene), but don't have the liver hazards associated with them. That doesn't make them safe, exactly, and they're vastly more flammable than the chlorocarbons, which is why they aren't used much as industrial solvents anymore - things that kill workers in five minutes in a plant fire get banned a lot faster than things that take decades to do the deed.
Modern low-VOC pump gasoline acutally has relatively little aromatic hydrocarbon content - EPA hates the things, so they're on the way out - replaced with branched aliphatics like iso-octane. There's no lead either, of course, unless it's avgas. It's distinctly possible that sticking your arm in pump gasoline is now better for you than sticking it in xylene or a chlorocarbon.
If I had one to choose, it'd probably be something like n-hexane. It's highly flammable and has a high vapor pressure, but it's a great solvent and is pretty cheap and not particularly toxic. Winter-blend gasoline should be close to that as well.
When I'm cleaining my own stuff, I usually use something like Stoddard solvent/varsol/kerosene initially in the parts washer, then, if it's sensitive, I rinse it with brake cleaner to strip the residual oil off. Sometimes parts go into the dishwasher - the detergent plus washing soda does a great job on kerosene residue.
For electrical stuff? I'd take it apart, find somebody running a motor shop, and see if they have an evap tank, dip tank, or something similar. An evap tank with the right chlorocarbon in it will solve your problem, and because you're not doing the cleaning, you're not getting the exposure. Don't know where such a motor shop is? Call the local safety-kleen distributor...