Just theoretically, as I never had a hot tub.. but I was close to once, and searched a little.
Salt is an option; will do some of the job chlorine does.
There was a successful trial on Iodine vs chlorine; done on professional swimmers pool.
Iodine, silver, salt cover most bugs. Borax cover fungus, the problem is algae.
Alternative is a copper rod in the tub. Also silver rods are used.