Your hair looks great, congrats! I live in a nation of primarily straight haired folk (HK), so I completely understand how a hairdresser who can cut non-straight hair is worth their weight in gold
I also have naturally wavy hair (it forms ringlets at the ends though, so it's technically curly-wavy, lol) & I've found that embracing my natural hair texture has taken a lot of trial & error, experimenting with both curly & straight hair techniques to see which combination works (many curl products are too heavy for me, but most straight hair products create frizz - my fussy hair needs the balance to be 'just right').
As for straightening or blowing out your hair at an appointment to check the cut, that's great if you actually plan to wear your hair in either of those ways - if you don't, there's not much point That's why I get my hair cut dry - if your follicles determine a wavy/ curly hair pattern, your hair will always wave/ curl in that way. Every time. My hairdresser told me that it might *look* different because certain strands clump together more or less with each wash, but you can generally predict where to apply hold products to discourage your hair from 'curling' in the wrong direction once dry (I have certain strands of my fringe that try to poke me in the eye, lol - others might deal with cowlicks, etc).
