In my experience with Illusive and other latex type items the first question I would ask is if the latex is hard. If it's hard or getting hard then it would need a more experienced person (Wampa most definitely) to tell you what to do.
If it's just starting to crack a bit but still fairly supple I have always used Johnson's Baby Oil (and ONLY Johnson's, others have mixed oils that will damage latex). Get a fine misting bottle and gently spray it on the statue and let it soak in. If it's like some pieces I saved it'll literally drink it up. Don't drown it though, just a fine coat and let it sit, and don't move the latex or it'll just crack more.
Sun is definitely the worse thing for those statues and masks. I had an original Tusken Don Post that was painted great...but the sun got it and it was shot, hard as a rock and started to crumble like Toht's face from ROTLA!