NOT SEA SALT!!! Not only does that have iodine, if there's a shellfish sensitivity, that would not be good.
Yes, definitely try kosher salt. I use a brand called David's. It has no iodine in it. You'd be shocked at the number of products which have sea salt in them.
My Sea Salt does not have iodine. I am using Morton Fine and they put a no iodine warning right on it. It is sea salt from Spain.