OK this is going to sound gross,
I mean realy gross but I would heal cuts and abrasions like that by covering the cut/abrasion with my own saliva via my finger and leave the wound open to heal.
Its what animals do and it works fine for them and funny thing is that it works fine for us too. Maybe that wound is a little big for you to want to try but next time you get a small cut simply lick it and let it air dry. You will be suprised as to how well it heals without any secondary infection.
Regards, Anthony