I'm glad things weren't bad enough to require stitches. I was never that lucky
I would keep washing him with the Vetericyn but after "disinfecting" him with that, I would put some sort of antibiotic ointment on the open wounds. Anything you have in the bathroom cabinet will work.
You want to keep bacteria out of those wounds as, sometimes, cellulitis can develop. It isn't that common but not all that uncommon either.
My friend's husband once spent two weeks in the hospital with a serious case of cellulitis in his leg. He had a cut and got fish guts in it while he was filleting a fish after catching it
If that wasn't bad enough, a couple years later her horse developed a bad case on his hind legs while she was on vacation and her over-21-horse-savvy niece was babysitting.
That cost a big fat vet bill, plenty of meds and days of cold-hosing but the horse healed and with no apparent kidney or liver damage.
I'm not trying to scare the boots off you, just want you to know what could
happen and it might be best to keep his wounds covered with an antibiotic