Unfortunately Southwest Florida is not the Mecca of iguana hunting and your biggest issue is going to be getting legal access. They are certainly here, but the majority are going to be in HOA communities or on private grounds. While no license is needed, you are required to have permission from the land owner to remove them. You can however hunt on 1 of the 32 commission managed lands, below is a link.
This interactive map acts as a reference for the general location of the 32 Commission-managed lands listed in Executive Order 23-16 and does not specify their actual land boundaries. Please check the specific area brochures for regulations and PDF maps.Explore the map:Hover over the locations...
storymaps.arcgis.com
Communities are going to want to see that you have a business license and are insured for the work. That leaves residential. You could post on a local group asking if anyone has iguanas that they would like removed for free. You may get some bites in Cape Coral, Estero, Bonita Springs and Lely in Naples.
You won’t see too many iguanas along the street channels / culverts in Collier and will raise eyebrows if you pull out an air rifle, doubly so within city limits. People are more relaxed in Golden Gate Estates, however there will be fewer to hunt. Keep in mind over penetration and pellet selection, it doesn’t take much to put them down. Lots of houses are close together and in some of the more affluent areas it wouldn’t take much to cause thousands in damage.
If you have access to a boat / kayak I could offer a couple other suggestions. Let me know if you have any questions.