One of the main reasons people try no-poo I think, eventually the shampoo doesn’t do it’s job as well, it becomes an increasingly futile routine to wash it before it feels dirty, itchy and generally horrible - I actually started showing my crown rather badly and my hair was horrifically thin, I was almost washing it twice a day because of the “dirty-itch” before I turned to no-poo, a stark contrast to what I have now. I haven’t washed my hair for… I don’t know, I think I started in Feb, I’ve lost track - There was one time when I was super sick and fell in a tub and went “stuff it”, but it quickly recovered.
The difference between no-poo and daily poo’d hair is very noticeable regarding thickness: Well hydrated and oiled hair looks and feels much thicker (not to mention shiny like a cruft’s dog-show).
I’d seriously avoid getting your hair dipped in any pool/hot-tub etc containing chlorine, this will strip everything out of your hair, it’s like the ultimate super shampoo, and often makes your hair super thin, brittle and frizzy, can take a while to recover with/without treating it - Investing in a swimming cap can make all the difference.
I honestly imagine short hair should be a quick fix with flour and a hair-dryer/straighteners > heat first > dip your fingers in cornflour, rub hands together, massage into scalp (once or twice, if your hair turns white, you used too much), brush down to the roots. Should be an easy 5~10min job.
If your scalp dries out, flakes or gets itchy, dip fingers in water, massage into scalp (should see very quick results <10 mins), brush through, when dry, should be nice as pie.
As for the hairdressers, just tell them you’re using dry-shampoo… I mean, they’re hairdressers, they should expect a non-laboratory-clean head of hair to wander in from time to time.