I had Iguanans for over 18 years and I would suggest that you use something like tissue or newspaper for their enclosure so that you can minimize the chances of bacterial spread. You can use the fillers in areas but leave palces for them to defecate....
However, we had our iguannas trained to defecate in the shower. In fact our Iguanan would walk to the bathroom and climb into the tub via screen made for windows(solar flexie stuff)...
The way we trained the Iguanas is to put them in the shower at tepid water temp and let them walk in the shower...good excercise ,too. After a little exercise they usually have to go to the bathroom and voila...all you have to do is sanitize the bathtub...it all washes away. You could actually make or get another shower just for the Iguana....I do question and think that the chlorine is not good for Iguanans since it absorbs thru their skin .
The Screen I am referring to is the screen you use to solarize your windows, comes in a long role at Home Depot or other hardware store. You can wrap it around the shower rail and let the Iguanas climb it also...and you can through it into the washing machine. You do want to make sure that Lysol or other disinfectants aren't around for them to get into since this is very poison to them.
Note of caution...make sure the water Temp is acceptable.
Warning...make sure the tub is draining...they can float but if the tub fills up they have to swim for a while...or drown.