You want to have the T4 (also called Total T4) and Free T4 tests done. However, it is really the T4 that is the most important test. It used to be thought that the Free T4, if elevated, was a good indication and confirmation of hyper-t even if the T4 was just in the upper end of the reference range, which is called the gray area for older cats. However, that is no longer the case. The Free T4 can be elevated due to other non-thyroidal medical conditions. So, sometimes the Free T4 test can just add more confusion for the diagnosis. The other important things for confirming the diagnosis if the T4 happens to fall into that gray area, would be the vet palpating an enlarged thyroid nodule, and the clinical symptoms. Weight loss despite a ravenous appetite is a very important one, which your boy seems to have. Post the test results when you get them.
It really doesn't matter if the source of iodine in the food is kelp or something like potassium iodide. It is a necessary ingredient in the cat food and should be present only in the amount that is required by the cat for good nutrition. It really does not contribute to the development of hyper-t. I wouldn't, though, give extra supplements that contain kelp since he is probably getting what he needs from the food.
Here is a link to an article by Dr. Mark Peterson, a veterinary endocrinologist who is considered one of the foremost experts on feline hyper-t. This article explains how to interpret the test results for feline hyper-t, especially when the results may be in that borderline gray area. http://www.animalendocrine.info/2013/08/is-high-serum-t4-or-free-t4-level.html
I hope this helps. You will still read older articles that say that an elevated Free T4 with a gray area T4 is confirmation of hyper-t, but that has been proven to not always be the case in more recent studies.