Hi, SimplyCause, nice to meet you.
I understand the nervousness. I shaved off my beard the day after I told my wife that I thought I was trans. It was the beginning of summer, so I didn't have to explain that on to anyone. But when I went to my doctor to ask her for a referral to a gender therapist, hoo boy, I was some nervous!
I was still fully presenting as male when I went to the therapist's intake interview. But, having gotten through my doctor's interview, it was a bit easier. And that's the thing: it does get easier each time.
I didn't like how long it was going to take to see the therapist in the public system, so I decided to cough up the bucks to go private. So, another interview. By this time, I was much more relaxed. After a couple of visits to her in male mode, I started dressing more androgynously.
You don't have to look feminine, especially when you are just starting. The professionals get it: they have seen it all before. If you think you are nervous now, imaging how hard it would be to go presenting as female, in public. No one expects that, initially, so don't worry about it. Save yourself the stress. Relax. Be yourself. You won't be judged on your dress and deportment.
They will want to know why you think you might be trans. That's all.
Good luck!