Where are you located?
How about boarding at his vet?
I'd go with the sister looking after him option. She may not get everything 100% right, but as long as he gets fed a few times, he will survive it.
He may not be in a good mood when you get home, but staying in his normal surroundings will be less stressful for him.
Give your sister a crash coarse in iguana feeding 101 and have a nice vacation. Deal with a grumpy iguana when you get home.