Your question is a little confusing. A general question if you should wear a condom just because you have a cut when having sex? You should always wear a condom for sex with someone that is not a regular monogamous partner, regardless of a cut. Small cuts, open sores, etc. do not transmit HIV. It has to be a big gaping wound. But if I were you, if you have casual sex or are with any type of sex worker, always wear a condom for vaginal or anal intercourse. (oral is not a risk). Anyway, with a limited post---- it's hard to know what you are talking about.
The ways that adults get HIV: unprotected vaginal or anal sex or sharing of IV drug needles.
I doubt the cut will last long but I would wear one until it heals.