Lewis,
when my guys cut them selves on building sites I always say the same thing. Doctor now, get a tetanus shot and check if stitches are needed. Doing this will eliminate serious infection and tetanus which will spread incredibly quickly in the hand area.
Having said that I have used insulation tape on a cut that went all the way to the bone before. Healed nicely albeit over several months. A stupid act but possible with a good immune system.
See the Doc.
