Seems to me the right tool to use is the tool that's made to do the job.
In addition to not bunging up the screws themselves, you might want a tool that won't accidentally slide out of the slot and land on the guitar top, which could happen with a regular screwdriver. The sides around that tool surround the screw so that shouldn't happen unless you really screw up.
There is such a thing as 'penny-wise but pound foolish'.
But more power to you if you can get the job done without spending the dough!
From what I've read from PRS, the bridge studs when not under string tension should rotate freely and can be removed with your fingertips turning the studs. The stop tail bridge is not a locking one like John Mann's intonated adjustable ones.
I do have a Swiss army knife with screwdriver blade that can help release the stud if it might be slightly overtightened. Then, simple fingertip twiddling can extract the stud as the thread backs out. The PRS Support page suggests a simple 25 cent piece will work as well. I'm seriously considering locating some .73 or .88 mm guitar picks that will slide into the slot and do the work. It was previously posted that the only thing that may be compromised regards a guitar pick is the pick, not the stud or guitar finish.
My plan is to use painter's tape over the bridge and the surrounding finish to keep the bridge in place, while protecting the finish. Then, measure the gap between guitar body and underside of each bridge stud, make note of that, then release string tension, then cut the strings. The only difficult part may arise if the studs won't rotate, which could happen. I'll have both the guitar picks and I'll find something comparable to what might work in a pinch. My stubby palm-sized screwdriver is small enough to control easily, still while turning the stud screws.
@dsenoj's idea of using an output jack plate might work, if I can find something similar without too much fanfare.
We'll let you know how this project moves forward, once the replacement studs arrive.