How To Treat A Open Wound On Finger Causing Severe Pain?

I have cut my finger quite deeply with a sharp knife. I feel no pain, and the bleeding has stopped, however the wound is not closed. I WILL NOT get stitches, because I have a severe phobia of needles. I want it to heal right. My question is this: Is it safe to use cyanoacrylate glue (superglue) to close the cut?