Your situation involves contact with an inanimate object which is not a risk for hiv. No worries, because you can't get hiv from personal contact except unprotected penetrating vaginal or anal, neither of which you did. Analysis of large numbers of infected people has proven that people don't get hiv in the way you are worried is a risk.
HIV is effectively instantly dead in air so the worst that could happen is dead virus rubbed you, and that which is dead cannot live again so you are good. Blood and cuts would not be relevant in your situation since the hiv has become effectively dead, so you don't have to worry about them to be sure that you are safe.