If you have a wound open enough for the coffee to get into the bloodstream directly, you won’t be drinking anything, much less coffee. But the amounts you’d be able to get in that way, it would be negligible. Not enough to have any increase in the effects of caffeine for sure.

Tbh, even if you’re holding the coffee in your mouth, have an open wound, and are applying pressure you force the coffee into the wound, you’re talking a drop of actual coffee that would get into your system. There’s not enough caffeine in that to do anything compared to swallowing the mouthful instead.

It’s one of those things where you’d have to jump through so many hoops you get even a single sip of coffee into the bloodstream through the mouth that it might as well be impossible. Just holding the coffee in there and letting any of the chemicals in it get into your system passively through absorption would net you a higher amount of caffeine than trying to get it in the capillaries more directly.