I cut my thumb on a cucumber slicer, need help!?

A couple of days ago I accidentally sliced a little part of my thumb. I put a band-aid and neosporin on it and I change it out every day. A little part of my skin (where I cut it) is still half hanging on to my wound. It's still not attaching to my wound. Should I just keep doing what I'm doing, and wait for it to attach, or should I rip of the skin? It will hurt if I rip it off though. Will my skin eventually attach back on to my thumb? Thanks!!