Honestly, I don't build the puppets this way -- I build them out of foam and leave the inside "Raw," and just slip the glove on before "showtime." The sweat doesn't really bug me -- I don't find it too much worse than doing yardwork or something while wearing work gloves. Nobody who helps me out ever complains, either -- but that might be because none of us have ever handled a puppet any other way.
I should mention, I've been a freelance artist for a few years and often wear latex gloves while cleaning up drawings, so maybe I'm just used to the gross feeling...
I am still learning about puppet building, though, so I am sure to try other solutions to this problem...