I have corrosively sweaty hands too. Thankfully, fiddle strings last longer than any of my other instrument strings (banjo, mandolin, guitar). I can turn a set of new steel strings black and rough and rusty within 20 minutes of playing. On fiddles, the aluminum winding tends to protect all but the E string. There are a few things I do to extend string life:
First, I always, ALWAYS wash my hands before playing and dry them thoroughly. I take regular breaks during playing to wash my hands again. In between hand washings, I keep a handkerchief or hand towel nearby to wipe my hands off. I also keep a microfiber cloth handy to wipe the sweat off the strings, neck, frog, and anything else I'm touching.
When I'm finished, I wipe my strings down with a cloth (including the undersides). I use FastFret, which is just mineral oil, to coat the strings and protect them against corrosion before putting the instrument away. If you put your instrument away with any skin oil, salt residue from sweat, or other foreign substances on your strings, they can eat the strings while you're sleeping.
On plain steel strings, when they start to get rough, black, and rusty feeling, I will either take them off or lay aluminum foil underneath them (i.e. between the fingerboard and the strings), and use Nevr-Dull to polish them up. I wouldn't recommend trying this on strings with an external winding, but it works wonders on plain strings. It makes them feel new again. Just make sure that after polishing, you completely clean and oil the strings.