The only way HIV can be spread in an adult is through unprotected anal or vaginal sex or by sharing drug needles with infected users. As long as you always use protection when having penetrative sex and never share drug needles, you will not get infected with HIV. Period, End of story.
No. As far as I know, it is impossible for you to catch HIV that way.
Relax.
I found a used band-aid with dried blood on it in my mouth while eating salad in a high-end restaurant and didn't catch anything I'm aware of. That was over 5 years ago and have been tested for all bloodborne illnesses since.
I think you're going to be ok. Imagine all the people who may have had an STD or other serious illness who handle money everday for many many years. If it was that easy to pass, everyone would be infected.