Just make sure you get all the loose particles off. Then make sure you clean the branch thoroughly for bug/insects. You can do that by baking, or soaking. The simplest way is wash them down in the bathtub and submerge to get any insects out.
Fake plants are cool but if there is a chance the Iguana can bite or tear pieces off you probably don't want that.
As Cedar and Pine chips can be toxic to these guy's, I would not recommend using a full branch from one of these trees either.. And as my logs inside my big cages would not even begin to fit into the tub or the oven.. I put them on 2 saw horses, scrubbed them down with pure bleach [that will kill any bug] and then rinsed alittle and let dry in the sun for a day. Once the bark is removed and scrubbed with the bleach, they turn a realy nice blonde color..