What I read of Gardasil is that it is only approved by the FDA in the USA for males up to age 26. Also, it is thought to be effective in preventing genital warts, but I am not aware of any data showing that it is effective in preventing cancers of the neck/throat. This would appear to be speculation and not science.
BTW, you can also get cancer, including those particular cancers, without eating any pussy at all, so to stop eating pussy based on some perceived cause-effect rationale, when there are a zillion other things you can be doing to reduce cancer threats like don't smoke cigarettes and don't drink soda with artificial sweeteners, to name just 2, is a bit of an overreaction.