+1 on the 'fake it til you make it' approach.
My buddy was terrified of cold approaches (as was I a few years back), then he saw this girl at the beach and wanted to talk to her. I'd been telling him for a long time to practice on a random girl. I told him "this girl is your random girl, it doesn't matter what her response is, just go practice your approach on her." And so he did...* and he pulled it off because there was no pressure to succeed. If you treat every girl as a warm up, as a way to practice for when the real thing finally comes along, your body will know what words need to come out even if your brain is paralyzed with fear,
* They've been in a relationship ever since. I don't think he understood the term 'practice'.