No one is totally immune - I am not sensitive, but I do get it. Spent two days cutting ash trees covered with it and burning the old stuff this summer, and was quite uncomfortable for a week or more after. Got it systemically from the smoke I suspect. I deserved it. Anyway, I use an axe to cut the vines off in the winter time, it creates much less chips and they don't blow all over you. But of course they're still there.....
I've read that the irritant is still active for a long time, but there's no doubt in my mind that old dead vines are less of a problem then fresh juicy ones.
Oh, and I second the jewelweed. And wash when you know you've gotten into it.