I do that all the time. My fingers split at the corners of the nails. When it's really dry and I'm doing lots of cleaning or working outside splits occur in finger joints and on the pads of my fingers.

Just clean real good, dry thoroughly then wait a few minutes to allow some additional air drying, then put on just enough to fill the crack and spread just a bit to either side. Once that is thoroughly dry I then use hand creme to moisturize the rest of my hands. I usually do this just before bed. By the next day healing has started and you don't get the shooting pain from those splits gapping and tearing more. It also keeps dirt and germs out while healing occurs.

Within a few days natural exfoliation will allow it to start coming loose and it will come of on it's own or you can peel it off.