Sure, go for it. Assuming you can clamp the shaft safely in a vise, cut the old grip off with a razor blade knife. Clean off the old tape. Re-tape if you want with the tape in the kit. I no longer use grip tape as I have found they install easier without it, they stick in place just fine and they're easier to remove without tape. Use plenty of mineral spirits to lubricate both the shaft (tape) and the inside of the grip. Slide it on! Make sure you eyeball and adjust the alignment right away.
YouTube has good how to videos as well. Good luck!