The island to go to if you really want to avoid the tourists is Molokai. It is the island where the leper colony used to be--so a lot of people find that out and "freak out" and avoid it.
There are very few hotels on the island for this reason--and it is probably easier to "get away" than on other islands--although I agree you can pretty much do that on any island--but then you can probably do that most anywhere in the world if you try.
So that you don't "freak out" about Molokai, for your information--leprosy has been eliminated in 113 out of the 122 current countries--and there have been only 100 known cases of leprosy each year in the United States since about 1995--and those are all from immigrants who come here from countries where the disease hasn't been eliminated--so don't worry about going to Molokai. There has been a cure available for the disease since the 1940s, first dapsone, then starting in 1960, rifampicin and clofazimine.
P.S. Your odds of getting leprosy are 10 times greater in New York City or London or Dublin than they are of getting it in Hawaii.