Sorry, super spotty cell service here. That’s a clean wound, and it will heal up just fine, I’m sure. I would just let him be. Keep him away from the other Rooster for a while for sure.
You will have to keep a very close eye on the two boys though. Are they about the same age? Have you got a lot of hens? What does your coop/run/ranging situation look like. Managing multiple Roosters together can be very challenging and things like this will crop up from time to time even with the best precautions (short of multiple separate runs). One key thing I look for is if one Rooster is being relentlessly bullied/pursued, or if after a brief showdown there is any severe chasing or prolonged confrontations.
My boys that free range together, (4) will occasionally flare hackles at each other, have a quick confrontation then they either have it sorted themselves or occasionally I will separate one and walk him back to his own ladies (they all have their own little flocks, and usually it goes just fine) but I know their personalities and they are all fairly laid back. One of the Roosters raised the two younger ones.
They all roosted together until one day my Rooster took exception to my Meat boy Rooster in a separate flock/roosting box, and had some very light comb damage. Then the two younger ones decide to turn on him together. It was a very rough day. I penned all the 3 boys separately, all day then kept the youngers separate from my older boy for almost a month. I increased my free ranging hens with them from 6 to 11, gave my older guy one mature hen, 3 POL, and 19 4-week old pullets to raise. They are all peacefully free ranging again together, for now.
So, although I think you’re good on the immediate injury/emergency care situation, there is still a fair bit to consider in where to go from here and what to do husbandry wise with your flock. Multiple Roosters can work, but it can also explode into far worse injuries that this. It all depends on the personalities and environment. That said, I also have 4 other boys that are all penned separately from each other with their hens... they just will not co-exist peacefully with one another. And I have a lot of space to free range.