In an emergency situation, I would go to the doctor!
But let's assume there is no doctor available: then it is not a very good idea to stitch up most injuries UNLESS it is a very clean cut. So ASSUMING your razor was clean, I would say the best things to do are as follows:
Short term: tape sterile gauze over it - after all, you are in a survival forum, I assume you have at least minimal first aid supplies!
Once you are taped up and can work without getting blood everywhere, the ideal things to do are, in my opinion:
a) throw a needle in a pressure cooker and cook it good.*
b) clean some fishing line with soap and water and rinse it well.
c) boil a bit of water and put it in an irrigation syringe (I have several around which I use to lube my M14s, but I also have a couple in the first aid gear pile.)
d) take off the pad, irrigate the wound. Hopefully it bled all over the place, because then it's probably clean inside anyway. Also, you will not be so careless in the future.
e) stitch her up.
f) put another pad on it and tape it on good.
g) wear a glove at work, if you do a job that gets you dirty. I guess if you work in an office that might not be a problem - I'm an ironworker and it would be a problem for me for sure!
Last year I got an axe stuck in my leg and didn't want to pony up for the thousand dollar plus hospital bill, so I just drove to an old doctor's place and that's about what he did for me. In fact the first thing I did was drive to the closest town and go to their hospital, but when they gave me a "for starters" price I hopped back out. The nurse looked at me when I stumbled in with my leg all bloody and said in a sympathetic voice, "chainsaw?"
"Axe," I said "Common chainsaw injury?"
"My three brothers and my dad are in forestry," she said. "You have the look."
Anyway, my grandma knew an old doctor in the same town so I went there.
"Axe wound, eh?" he asked.
"Why...operating a hop-in clinic?" I asked. He cleaned me up, stitched me up, I watched for signs of infection, of which there were a couple, but not very bad, so I put hot packs on it every night for a few hours, reasoning that I could make a spot-fever that my body could never match. The infection went away after a week or two, and I took the stitches out when it was definitely completely closed. It took almost two months to be completely painless, though, which I attribute to the slightly primitive medical care.
*I guess if I didn't have a pressure cooker I would heat the needle up with a torch? But you know, I might just as likely wash it carefully with a scrub brush and soap and water. Also, I hope you had gloves on for handling everything once it was good and clean!