I'm guessing (without seeing them) assuming that they are small firm and irregular shaped that they are benign sebaceous adenomas. There really is no way to remove these masses other than surgical removal. There are variable surgical techniques including scapel (cutting) excision, laser excision, or cryotherapy. I am guessing that they aren't really causing any problems except for if they get bumped and dislodge and start to bleed (and they probably don't look very attractive).
If you can't afford surgery I would keep some styptic powder handy to help intervene in the case of a bleed. Your vet may even feel comfortable sending you home with some tissue glue to help seal up a bleeding wound if you were having trouble getting it under control.
Since these aren't really warts they are not related to a viral infection and therefore anti-viral medication isn't going to be effective. Your vet is correct that they may very well come back or more may pop up in differently places even if the ones that are there right now are removed.
Cows do get papilloma virus (warts) however warts are very uncommon in dogs (I have yet to see a dog with warts in 12 years in the field) and therefore wart medication most likely would not do anything for these lesions.
There is some talk of Vitamin A (or retinoid medications) supplementation reducing the likelihood of more of these lesions developing but I would discuss this with your vet to be sure it is safe for your dog. Vitamin A can affect liver function and tear production in the body and it would be unfortunate to create a new (and potentially more serious) problem while trying to fix the original problem.
This site talks a bit about sebaceous adenomas and other masses that are similar in appearance:
Please let me know if this helps or if you have any more questions or concerns.
Dr. Sarah Duncan