.... if you want to be safer disinfect it before.
It's funny I never care about infections. I neglect the wound almost on purpose. Once though I was a bit worried, my arm got very warm, red, swollen and hard about 3, 4 days after cutting.. I went to a pharmacy, the druggist treated it and told me to observe and eventually go to see a doctor. Was uncomfortable because she noticed that it was self-inflicted and looked at me pitiful.