I’m exactly the same dude. I suck at cold calling and I become self conscious and worse when someone points it out. Just don’t worry too much about your stuttering. If it happens, it happens. Who cares what someone else thinks. I came to this conclusion that it really doesn’t matter as long as you can get your point across in the end. Also, it helps to build and maintain your confidence so you’ll seem more composed. Once you have your confidence down and stop worrying about your stutter, it should die down a little bit. This helped me. Good luck.