There isn`t any direct problem about using salty water in a hinoki bath as long as:
1) once tub is emptied, it should be generously washed with normal water to avoid oxidation and staining
2) we will use stainless screws and plates, so no problem.

Anyway we do not have experience of this and do not know what it will happen in the long span. It may be OK, I do not know. You would have to try at your risk. I feel that salty water would at least alter the aroma and therapeutical properties of hinoki, but this might be just our prejudice.