The hot tub is not potable water. It also need not be "new" water - IOW, it can be reused for a while, how long depending on how cleanly participants make themselves before soaking in the tub. Thus, it appears to me that: W/the caveat that the water cannot be actually poisonous, or irritating to most people, you can use chemicals in the water to change it's behavior. This is offered as a concept only because I'm afraid I'm not knowledgeable in this area of pool and public bath treatments, nor in the area of chemical activity in heat exchangers.
Another concept: As you know, the heat exchanger is the place most of the problem will occur. The higher the temperatures there the more lively the chemical activity will be. Thus, keeping temperatures a low as possible in the heat exchanger may give the longest run time between maintenance. If you want water in the tub to be 115F, then limiting exchanger temperatures to 120F will greatly reduce chemical activity compared with running the exchanger at 140-160F to mix the tub temps quickly. But that may not be possible for you. The trade-off is, of
course, that it will take a long time to heat the tub initially and you will want to insulate it and all plumbing as well as possible.
However, since
wood burns hot and you probably want this
hot water to be on demand, you might consider an indirect system to allow you more BTU input from your wood boiler. A two stage heater, where special fluid (distilled water or some other favorable concoction - consult the manufacturer and the pros) can be run in the boiler and the heat exchange can be done in a coil-in domesticate hot water tank. The boiler temperatures can be higher and it's heat exchanger can live in its own little sealed world. The storage tank which is where the tub water would be heated _might_ be a lot easier/cheaper to maintain.
This seems like a problem worth running by a _good_, experienced hydronic heating professional. Unless you just want to light a fire under the tub, which could work for a while, I guess, but the tub would likely have a short life. The wheel _has_ been invented before and a good pro (and you might need to talk with many before you find a likely fit) knows what concepts, equipment and techniques apply and how to balance your design goals with safety; they also can offer you workable alternatives. I haven't visited for several years so the place could have changed some, but "heatinghelp.com" used to host a small group of such people who willingly provided advice at all levels; IIRC there were one or two who installed wood systems, but it was not common.
Depending on the system you use, you could create several kinds of dangerous risks. Please take this seriously, as you are potentially dealing with a complex high temperature, high pressure system. As I understand it (I was a plumber, not a hydronic guy) wood burns hot and it's relatively hard to regulate, so safety is a very important part of the design - when something doesn't work just perfectly, you don't want to turn a storage tank into a bomb or split a little connecting pipe and spray around 300F heating fluid.
Regards
Rufus