O.P.,
I have a Blueberry farm. Poison Ivy is a constant fight.
We prune in the winter. We get Poison Ivy and sometimes BAD.
If ya mess with the crap, wash your clothes with a strong degreaser, then again normally, then one more time empty of clothes with the degreaser.
And then... Maybe one more time, and darn sure before your wife goes and washes her stuff. Women have NO sense of humor about some things.
One thing that might help with your tree is a "Booger hook".
I use 'em to Kill/cut vines between bushes in growing season, to keep from trashing fruit pulling vines and when I can't use herbicides.
Take a broom stick and cut a slot about 3" into the end.
Then dismantle a Cheapo Linolium knife, insert the tang of the blade into the cut, drill it, and run a screw through it.Then wire wrap it tight. Done.
Just hook the vine and pull. Ya never have to touch the stuff to cut or remove it from where you have to work.
Just remember that the little hairs from the vine are still there, so there will be some exposure, and any wood cut, the saw, and the chips are contaminated. You will get it, just not as much as if you were farting around with the vines directly.
Did I mention I hate the crap?
Stay safe!
Dingeryote