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Small nicks you can use sandpaper or a pumice stone to smooth out. I used a barber hone one time to take a few small nicks out of the strop edge as well. If you get a cut you can use rubber cement...

Another possibility. You can get an American vintage razor, shave ready and a strop for $55.00. I don't see this mentioned much here, but it seems like a good deal for someone starting out.

The...