Now if you are looking for a way to transport a very large (or not so large) iguana to the vet for example, I've found the best way is a very large and long underbed rubbermaid container with locking top. You can get a clear one so he can see out, and you can poke ventilation holes in the sides using a heated butter knife. I heated one by slipping it under the heating element of an electric stove and handling it with an oven mitt.
I put heating pads inside, and blankets on top of the entire thing once it's positioned in the back seat of the car. The heating pad cords just snake up and out underneath the locking top, with the controllers on the outside of the container. I use a power converter in my car's cigarette lighter to power the heating pads. It's worked very well for me.
For basking and short walks, my iguana's leash is the least expensive, most valuable investment I've made towards his care. I have not had any spine or scale problems with this type of leash, which secures tightly around the hips of the iguana. It costs less than 3 dollars to make. We live in a big city, and the leash has prevented him from jumping or running where he should not and probably saved his life.
Get a length of cotton cord, similar to the cord that cinches the hood of a sweatshirt. I got mine from the craft/sewing section at Walmart. You will also need a barrel clasp. This is the kind used in sweatshirt hoods, also. It looks like a tube with a hole shot through the middle. You squeeze the top and bottom of the tube to release and lock the cinch cord on the sweatshirt hood. Also can be gotten from Walmart or a sweatshirt you don't want anymore.
It's also useful to have a caribbeaner (maybe spelled caribiner) hook like climbers use. This way you can clip the leash to your belt loop and the iguana can sit on your shoulder, leashed, and your hands will be free. They sell them at the hardware store as keychains.
Tape the ends of the cotton cord so it's like a shoelace. Depress the top and bottom of the barrel clasp to open the hole in the middle, and snake both ends of the cord through the hole. It's not easy. I poked them though with a safety pin or a match. You should now have a loop of cord closed by the barrel clasp.
Knot one end of the cord. Tie the other end to the hook. Pull and adjust the cord so the long end is the one with the hook at the end. The hook end with clip to your belt hook, and the loop will go around the iguana's hips. Adjust the loop to fit your iguana. The knot should be right up against the barrel clasp. The loop should be tight, but not too tight. Your iguana should not have trouble breathing, but you should NOT be able to slip a finger between your iguana and the cord.
Now, the way I see this leash is not as a fool proof device, but as something that's going to give me a few extra seconds to grab my iguana if he spooks or tries to jump on an interesting looking stranger. 
Do not leave your iguana unattended while he is on the leash. Don't let him run around. The best thing to do is to let him climb around on you or sit in your arms and bask.
You should not put your iguana on the ground outside on the leash. They are more likely to run and gator roll, because the ground is not where they want to be and everything looks huge to them from down there. If your iguana is gator rolling and misbehaving when he has the leash on, you may have to acclimate him to the leash indoors using treats and positive reinforcement. Perhaps take only short trips outdoors and lengthen them until he doesn't mind the leash.
Good luck!