About 10 years ago I had the bright idea to remove a large thatch of poison ivy while it was dormant one winter. My yard backs on a creek and there were large vines in the trees overhanging the bank. I wanted to cut out the vines at the ground level to kill the upper vines in the trees and then I'd keep track of the ground level (in those days I was still using Roundup for a few things.)
I wore gloves and long sleeves, but I was handling the vines and they ooze the juice when cut. It got onto my sleeves and was against my skin long enough to create a huge breakout. I itched for weeks even with the shot and medications.
It's a project that you need to plan carefully. I don't know how your poison oak compares to my poison ivy as far as the size of the plants, but if you do it, be sure to clean off all of your tools handles and blades (use a strong mix of detergent and water or perhaps straight isopropyl alcohol) after cutting and touching the plants. Without the leaves there is less to brush against, but what you're dealing with is a lot more toxic so try not to touch them at all with gloves and if you do, throw out the gloves. I use those nitrile-coated work gloves
to keep things from soaking through onto my skin, but I would still throw out the pair I used for this task.
My adventure with the poison ivy was bad enough that I am now very sensitive to it. I did it to myself, and I have to go into the doctor for a shot, lotion, and prednisone
tablets if I get into it now.
Longer answer than you had in mind, but perhaps it will spare you the situation I set up for myself.
Good luck! Below are the gloves I mentioned: you can get a 10-pack for about a dollar a pair at Home Depot. Get them in the hardware area, not in the gardening area (gloves labeled for garden use cost more for some reason.)