I wouldn't worry. I have really klutzy chickens that always seem to have bumble foot in one form or another. This summer I had 4 hens and a rooster running around in brightly colored vet wrap booties. I think they actually like them, especially the bright colored ones. I saw more than one hen lift her foot and look at it like, "That's COOL! I LOVE Pink!"
Seriously, I agree, if you have concerns, wear surgical gloves. You can get a box for next to nothing at Wally World. And definitely wash well with hot water and soap. not only your hands, but your arms as well. I'm a retired nurse and the hand washing is just second nature to me anymore. You should be washing after handling your ducks or chickens anyway so no big deal.
Technically, yes, staph is contagious. But the risk if you don't use common sense hand washing after treating your duck's feet, even if you do wear gloves, wash up afterwards.
That poor baby sure has himself some nasty looking feet. Sure hope he gets feeling better soon. Keep up the good work.