I would say find a cleaner place...
I was going to say that if you feel it would be necessary to bring disinfectant, then that is about as good an indication as you can get that that particular salon and you are not a good match.
And if you can't find one that you would not feel the need to provide with disinfectant, and that you can afford, I would suggest the DIY option.
Because I am so ticklish, I was never able to get my feet done in a salon anyway, and of course now, due to diabetic peripheral neuropathy, no salon would touch either toe or finger, nor should they, so the skillzz my ticklishness obliged me to develop from pre-teen age onward stand me in good stead today!
Edit to note that I have noted in recent years that even the smallest and cheapest hole in the wall salons in my hood have taken to not only using disinfectant, but also using disposable liners for anything peoples' hands and feet get dunked in. I know they can't be expensive, because I know people who work at these salons, which is how I know they use them, since I don't go there to get my nails done!
Anyway, what you might do is google, and find out the name of a company who makes these liners, and put in a request for literature, and give them any name you like, but the address of that salon!