I think for me since I've done so many trades (in NL and NH), knowing exactly what will happen helps a lot. I have anxiety too, and whenever I have to do something in real life that makes me anxious, I like to research it or plan it out in my head beforehand so I have a general idea of what is going to happen. For AC trades, its easy- arrival, greeting, transaction, thank you, goodbye. And that's it! You can keep it short and sweet, or you can add other comments like, "I like your entrance," or fly over, etc. Also remember you can always say no if someone asks to visit your shops by saying something like "sorry I'm in a rush!" or "sorry I'm busy irl!" or something. And also like I said before, people are likely thinking about their next trade rather than thinking about you specifically.
Also random addition- something that helped me overcome anxiety provoking situations in real life was reminding myself that "it doesn't have to be so bad." Most of the time when I am anxious about something, I really work myself up which adds to my growing anxiety, and reminding myself that I am the one making myself feel this way (making my heart race, hands shake, etc) really helps adds perspective to the situation, meaning the situation itself isn't making me feel this way, I am making myself anxious. Does that make sense? Lol