One of our coastals we bought with a retained tail tip shed, My own stupidity, I was told he'd only just shed, and didn't bother to check it there, got him home and got the retained shed off and was left with a stump with what looked like blackened bone sticking out of it. He wasn't in any pain, it wasn't tender to touch and since it was actually an open wound, I didn't bother taking him to the vet. It's since healed up just fine, it looks a little wierd but only if you look closely.
To the OP, I'd suggest keeping him confined, as in take out his branches or anything he can climb on so he avoids using his tail, and putting him on newspaper or similar, it's a lot easier to keep clean and hygenic. Snakes are pretty good at not dying most of the time, and I can't imagine that things like this would not happen in the wild, so theoretically it should heal without any dramas. And before anyone starts going on about captive snakes not living in the wild, I'm well aware of that, but honestly, if this happened to a wild snake, it would probably heal up just fine, and nature's grotty and disgusting, so a captive snake in a box should have even less dramas. I'd say still take him to the vet, but don't stress out too much, he should be just fine in the long run