BB guns are not that effective and don't usually kill the iguanas. The Iguana Man frequently captures iguanas (noose on end of fishing line) that have signs of lots of BB hits. You need at least a pellet gun air rifle. Problem with that is you will eventually have the cops called on you. Or, even worse, a homeowner thinks you have a real rifle and takes matters into his own hands.
Air rifles using pellets are okay for unpopulated areas but in heavily populated areas such as here in Broward County, you are asking for trouble using air rifles to hunt iguanas.
I’ve heard of people traveling to Costa Rica to hunt iguana with air rifles. Sadly, there were none when I was in S. Florida. A friend came back, recently, and said they’re all over the place. I’m surprised people aren’t eating them.
Brother and I worked that out as kids of the 60's.
We got skilled at hitting birds and lizards in the head. We shot until the target was down.