Potassium Permanginate.
If you DO go this route, be sure not to use any other products containing glycerine. You REALLY won't like the reaction.
I recommended Isopropal alcohol because it's a safe, low cost, and effective antiseptic.
If the infection is minor then most of what has been recommended will work just fine.
I think that we might assume that Scarpi's finger is not bloating up to the size of a knockwurst. Even if he does nothing, then his body's immune system will take care of things. He is describing something requiring the same caution that you would give to a boil. Antiseptics will just speed the healing along.