Heya Hope! Let me make use of my horribly boring medical school education and perhaps shed light on what kills HPV.
From what I learned in Microbiology, most bacterium/viruses that can be classed as STDs are killed by two things: dryness and cold. Let's get even more boring: bacterium/virus STDs are often very fragile critters. Tough bacterium often have an outer layer of protection, a capsule, that shields them from the environment. Contrary to bacterium, viruses come in enveloped and non-enveloped forms---tough viruses are actually naked.
STD critters either are capsule-less bacterium or enveloped (delicate) viruses. Both are susceptible to drying and cold, and the outside in general. They just don't last very long in the elements. So anything you could think of probably will kill them: conventional soap, steam/heat, disinfectants...I don't know about whipped cream, but probably
HIV is the epitome of fragile: for all the viciousness that it is in the body, as you said it dies in seconds outside of it. Not sure if the other STD bugs are this wimpy, but they're much more delicate than non-STD critters.