I'm the same as you, I've inherited my mothers fluffy face and I hate it!! I try and stay out of any light so it doesn't show my beastly face haha.
Just as a precaution, I would take some antihistamines a few days before, and apply sudocrem to your face afterwards. I get a really bad histamine reaction when I wax my face. The last few times I've done this, and it's been much better. Saying that, I wax my mums face all the time and she never reacts. If you're worried about the hair growing back stubbly, then I wouldn't worry. Mines grown back exactly the same.
Just make sure your therapist really stretches the skin, it's very easy to graze on the cheeks when facial waxing xx