From how it sounds, he should probably be okay without a vet, but this is exactly why you need to find one pronto. This stuff just always happens with no warning and next time it will be something more serious... consider this tail episode a warning for you to find a vet SOON!
My iguana lost half his tail this past winter. I did consult a vet, and this is what he said.
1) Keep it clean. Flush the wound with sterile saline (like what you use for contact lenses) and give frequent baths. No rubbing alcohol!!
2) Apply triple antibiotic. I used Neosporin. Just squirt a huge blob on the mess at the end of his stump every time you can get him to stay still for a second! Since this is a bigger type wound, DO NOT use an antibiotic cream with hydrocortizone or any type of cortizone or cortisol in it.
3) Don't even bother trying to bandage it up. It'll just promote infection, that is, if your iguana doesn't tear it off first.
4) Mostly, just leave it alone. All those muscle bundles you see sticking out like threads or pointy pieces of meat will knit together into a scab, you just have to be have faith. They kind of dry up and fold over on themselves.
5) Keep a strict eye out for swelling and oozing or smelliness or any kind of pus. There shouldn't be any of that at all. This is where having a vet comes in. If you notice any of this at all, your iguana is going to be in a lot of agony if you don't get him to the vet.
The swelling part is actually hard to determine sometimes because what will happen is a soft black bump will form at the end of the stump, and it kind of looks like a pimple. It's new growth. That will lenghten into (hopefully) a new tail, or something like it.
I will follow this with some pictures of Bud's regrowth. I just wish I had taken more! I know it's kind of upsetting, but if you can, try to take pictures of the tail every week or so, it could really help someone in the future.
Also, I would take this opportunity to figure out why the tail fell off and fix the situation. Why do you think it happened? Bud's tail was lost because my petsitter handled him improperly and scared him.
-Erin