Well, you will find a big difference between threesomes that are primarily about sex that may include friendship and caring, and triads or V's, which are primarily about the relationship.
If it's the first definition, then while you may find folks on here who are interested, you may do a lot better on boards dedicated to swinging.
So, if I understand you correctly, no HPV1 or HPV2 in your prospective partner. This would mean that they would need to be tested explicitly for those (since those don't normally get tested in the normal raft of tests). Have you guys had those tests done on yourself?
"Listen, or your tongue will make you deaf." - Native American Proverb