HIV risks for adults are:
1) having unprotected, penetrative, anal or vaginal sex, or
2) sharing intravenous needles (with IV drug users)
NOTHING else you can think of is a risk for HIV, including the event you mentioned. Blood, once outside of the body, is no longer infectious. If a person could get infected with HIV in this manner, everyone in the world would have HIV by now.
There is no detail you could add to this event that would make it a risk for HIV. However, touching an object you find in public, and then touching mucous membranes like those found in your nose, is a good way to contract serious viral illnesses like the flu.