For most prints, especially when I'm working up to a fine print and developing one-at-a-time, I use 30+ year old bamboo tongs with rubber tips. I've replaced the tips a time or two, but am still using my very first set of tongs... it's kind of a nostalgia thing.
I submerge the print by sliding it into the developer face-up, then proceed to gently push down the floating parts of the print with the tong tips, which I continue to do throughout the developing time. This is the agitation (sorry, Chris, I'm an inveterate "tong-poker") along with an occasional flip face-down and then face-up again. Gently is the key word here, but I've never had tong-caused defects. I pick up the prints with the tongs by a corner (I always have generous borders on the prints) when transferring to the stop (slap, face-down in the stop bath) and fix. For larger prints I often use two sets of tongs; works fine up to 16x20.
However, I don't hesitate to use my bare hands when I need to. 20x24 prints or prints in batches that need to be shuffled or when one sticks to the bottom of a tray and I can't get the tongs under it to lift it all require hands; sometimes I just feel like using my hands. The main reason I don't use my hands a lot is simple convenience; I don't have to wash them so much, and I do reduce my exposure to any developing agents that I might end up developing an allergy to (Metol). I don't use toxic developers like Amidol or even a lot of Metol, mostly PQ developers, sometimes some Glycin. I wouldn't hesitate to use nitrile gloves when printing if I were worried; I use them when negative developing since I use Pyro film developers.
When I do get print damage, it is usually caused by other things, not handling in during processing.
Best,
Doremus