Larry, here are some options. Those "suspicious" three-leaflet things are 99.9% sure to be PI. Before you start messing with the stuff, think these over carefully. I've been battling a bumper crop of PI and eastern poison oak too. It really seems to be a problem this year.
1. As said above, hire someone else to remove the hedge.
2. Wait till winter, after the foliage drops and the plants go dormant, and then go to work. This doesn't prevent the PI problem, but will minimize it. The leaves are the worst problem, though the stems and roots do carry urushiol too.
3. If you don't care about the hedge, spray glyphosate (RoundUp) all around the area you are removing and allow it a week or more to do its job before you begin work.
4. If you do care about the hedge, try the Ortho product that is meant just for PI and then follow No. 3.
No. 5 would be to follow your original plan, but I can't call that a real option. Nor do I see why it would be so important to pull up a hedge now, when everything is in full leaf (unless you have legal reasons, such as a municipality or homeowner's association hassling you about the hedge). My chainsaw and other serious yard work waits till cold weather; the only exception is mowing. But I live in the boonies and have that option.
Final thought: watch for Virginia creeper, which has five leaflets arranged a little like those of a cannabis leaf. Creeper is in the grape family, not directly related to PI (which is in the cashew family), but can cause a severe, scarring reaction with susceptible people. It's at least as common and invasive as PI and loves to climb too. Around here and probably there in Pennsylvania as well, Virginia creeper is a "marker plant" for PI and vice versa. If you have one, you are very likely to have the other. Since you have PI, you probably have creeper too. Be careful.
My mother is immune to PI. My father and brother are not. I don't know about myself—but I'm not trying to find out the hard way either. Therefore I don't get close enough to it for skin contact. Neither should you if it's avoidable.