Personally, I find nylon strings painful after having played steel-string acoustic and electric for years. I think it's what we're used to, and that we can get used to pretty much anything if we want to bad enough.
As for alternative strings for an electric guitar, any string that can disturb the magnetic field generated by the pickup's magnet, and induce a current in the windings could be used, however the question at that point is whether the string and pickup combination would sound anything like you expect.
As another answer says, Billy Gibbons uses .007, but he also has a bank of graphic equalizers and frequency analyzers which let him adjust the tonal response of his pickups and strings to push them back towards a beefier sound. If you watch him play, he has a wide range of guitars available to him, from Telecasters to Les Pauls, but they all sound very much alike, which is impossible normally, since their bodies, necks and pickups are so different, but the electronics adjust their output to match his famous "Pearly Gates" Les Paul sound. It's a very high-tech solution that most of us can't afford, though a decent 10-band equalizer can help. (You'd really need one for each guitar you use to do it right.) In Gibbons' situation, this solution works nicely; I saw him playing live a couple years ago, and he's got an amazing sound.
Players like Stevie Ray Vaughn, opt for heavy gauge strings, because the more metal moving through the magnetic field of the pickup, the fatter and more powerful the guitar signal. Various blends of nickel and iron in the metal of the string affects the overall sound output too, but it's the gauge that makes the bigger difference, so the lower the gauge, the less metal and the less output which translates to a thinner sound.
I switched all my guitars to .010s after having used .009s for years. The first couple weeks were weird feeling, but now, after a couple months, they feel pretty normal. My fingers look all gnarly with the giant muscles they now sport... nah... not really... my finger tips were a little sore for a couple days, but everything feels fine and I like the added "beef" I get in the sound of my pickups.
So, to reiterate:
- Nylon is out because it's not magnetic.
- I doubt you'll find an acceptable sound from any sort of "silk and steel" strings because they're not going to disturb the magnetic field that much.
- The lighter the gauge, the less output and subsequently, your guitar will have reduced bass and mids.
It's physics you can counter using some electronics, but I'd really recommend sticking on .009s and let your fingers adjust.