1. Are there any squamous papillomas (or similar growths that would look the same to pathology) that are not related to HPV?
A: Herpes, so benign growth from HPV is "better", in this case.
2. I have read that squamous papilloma is not contagious (low virulence). Am I contagious in general with HPV?
A: There's always a risk you've spread this to your wife, however, assuming you had this first, her body may have already fought it off where as your body may be still working on it. Expect 2 to 10 years as an average clear time for your body to fight it off completely.
3. Once the papilloma is removed, am I contagious?
A: No, same contagious factor as prior to it forming. The papillomas are just the surface. HPV like HSV is at cellular level. If it creates papillomas, it's low cancer risk but aesthetically undesirable.
4. If it is still contagious, what are appropriate steps to take to ensure my family's protection?
A: I'm like you where I'm a sort of an ocd germa-phobe. I found out after seeing countless doctors for autoimmune issues I started tying into my HPV 53, that doctor's don't give a hoot about HPV unless it means pitching a vaccine for it they can profit from. Why? Because HPV is common. The fact is, HPV is classified as sexually transmitted, but you could technically get oral HPV just by sharing a straw with someone. It's not worried about because no matter the risk of the strain, the clear time is always 2 to 10 years, and between that time, you may see papillomas from time to time as your body is battling it. Have them removed if they appear, if they don't, great. HPV types that create cancerous growths on the other hand are the most successful cancers to eradicate, but that's worst case scenario. Just realize that your HPV could have come from your wife, or considering the clear time span, just prior to being with her. Let's be honest, it's from eating the peaches we've been eating. Figuring out which one had the pit however, is irrelevant.