I'd do a bit of research to see if that "wound seal" stuff works when you're on blood thinners. If it activates whatever clotting factors are there, then it may just make for lots of red sludge instead of a sealed wound.
Or, just use CA. Whatever you do you'll probably get a hell of a lot more bruising than you would without the blood thinners, so using a chicken stick (or wimping out all the way and using an electric starter) may be the way to go.
I just wear a glove. That way in the event of serious incident, all the pieces will be in one bag.