Is it a cyst or a wart?

[Notsosure91]

My boyfriend had a small bump on the tip of his penis appear a few months ago. He went to the free std clinic and they told him it was hpv, and they have been treating it once a week with acid. It hasn't gone away or changed much. I have told him multiple times to see a dermatologist, because it might not be a wart at all, since after it appeared I immediately went to my OB and got a Pap test. It was normal, and I have had the guardasil shot - hpv vaccine.
The bump he has does not look like a wart. I have had them before on my feet from the gym, and it looks nothing like it. It is not rough or cauliflower like, but rather soft tissue, almost like a scar. It does not have visible fluid and if you try to pop it it will only bleed. I have a sebaceous cyst on my neck and I told him I believe that is what it is, but he is continuing to get treatments with the acid and refuses to believe it is a cyst because they are "professionals". The bump is perfectly round, soft, and only slightly raised, maybe a millimeter above the skin. Could it just be a cyst? And if it were a wart, wouldn't they treat it by freezing it instead? Any input would help. Thank you.