It is true (according to sources that are credible yet no longer readily available to me for quoting directly due to my misspacing them) that long-term use of the hot tub tends to increase cancer risk by over 400%.
So, though the chlorine amount is insignificant for what would be termed a "poisoning" that causes short-term right-now symptoms, long-term use is certainly not a contribution to your "health account" but rather a "withdrawal".
I seriously doubt that what activity you engage in while in the chlorine-style hot tub really matters at all. The skin is absorbing the chlorine systemically, its temporary presence in the vagina is probably inconsequential.
So, in summary, if your going to be spending time in a hot tub anyway what you choose to do there that would otherwise be deemed healthy is most probably not going to further subtract anything at all.
So, unless you are spending lots of time in the hot tub simply for your reason stated above and you would otherwise not be there at all, it really doesn't matter.
Avoiding exposure to chlorine in virtually all it's forms is certainly a good idea. Good thinking.