It's a virus, not a disease. Not that that makes much difference to how people feel about it. Also, you have/had a strain that people are a little more leery of - the genital warts kind. It's one thing to have an HPV strain that give you foot warts, or no warts, but I think potential partners would be really annoyed if they caught genital warts. The only kind I'd be more annoyed with is the type that is directly linked to cervical cancer.
While it's true that there are strains that cause no warts which means people could have it w/o knowing it, but I think in this case (where the virus produced detectable genital warts) assuming they may already have it isn't fair.
Could you ask your doctor if there's a specific test to see if the virus is still active in your body? Getting a PAP test only looks for changes in the cells of the cervix, one of the results of certain strains of HPV, but doesn't say anything about the presence of the virus in general (it's correctly assumed that if you have cervical changes, that you have HPV). Mainly, not all strains cause cervical cell changes, so getting a clear PAP isn't a definite 'all clear'. I hope I've made sense, I'm tired...