Separate the action from the result: write the message before adding the recipient, say aloud you don't care what happens, or schedule the send.
"What if I'm too salesy?" I hear that one at least three times a week. What if they don't respond? What if, what if, what if. I do it too: better not to talk to them at all than face what might happen. Babe Ruth said his approach to home runs was to swing as hard as he could, right through the ball. Whether it cleared the fence was largely out of his hands. What happens after you press Send is out of yours. These three tricks put a little distance between writing the message and worrying about the reply.
Pick the person you've been hesitant to message. Write the note in a blank draft with no recipient, so it's just words on a screen. Add their address, schedule it for five minutes out, and close the app. Then go get a taco.