Honestly... if there was something you could buy from a store or pharmacy to just make it disappear... the creator would be a millionaire. There is no such thing. That's the bad news out of the way... but there is good too
Chase has some good articles on here about using peripherals and also pre-opening. I think understanding these things go a long way to getting over the anxiety. It's not really about the anxiety, its how you think about the situation.
I'll give an example. Guys sometimes build up the whole idea of the approach, where you see someone across the room or the street, then in full view of everyone watching (they aren't really), march across and boldly state your intentions. It sounds nerve wracking! But it can also seem un-natural. This weekend for example, I met a gorgeous brunette. She was across the room with her girls and getting a lot of male attention. However I was out for an event so I was dressed to kill. I saw her looking at me out of the corner of my eye a few times but we had just arrived, I kept having banter with my group of friends. One of my buddies even commented though, how this girl was checking me out as my back was turned. So we know it's on, right?!?
A lot of guys were going over, taking pictures, doing the march across the room. She wasn't blowing anyone out, but she was humoring them before moving on. So how do I differentiate myself? She's already seen me. I haven't yet done anything like the other guys but... I haven't done ANYTHING yet really except show a little social proof.
Easy! I kept my group lively, but sort of worked them half way across from where we began, next thing I am basically standing to the side of her group. Of course she moved from her perch and "Ooops!", she bumped into me
Next I turned over my shoulder and said "Hey, I need a quick opinion, but wait, I've got to go soon!"... as I took a half step away... "Who lies more? Men or...." Hahaha, Nah, I didn't actually do any of that

She bumped into me (girls do this deliberately a lot), I turned, gave a warm smile and said "Hi! Who are you?". The rest is history.
That was a long ass way of saying... make it easy on yourself!
The BEST girls to open are those who've already noticed you and WANT you to approach!
And if the idea of the "big approach with everyone watching you" seems terrifying... just put yourself in a position where all you really have to do it turn to her and say Hi! Nothing un-natural about that.
I know Chase has some articles on it. Gambler describes this in his Naturals videos too, I think they're on YouTube.
And co-incidentally... The Behind Day Game channel on YouTube recently put up several videos about overcoming Anxiety and Excuse making. Short simple videos but they just push the point home. Very nice.
A final point. Someone said this to me recently...
Most guys aren't actually afraid of approaching, they aren't afraid of "What to say".
But they ARE afraid of... What to say NEXT! The 2nd thing!
If that's the case for you, there's no harm in going through a few scenarios in your head and thinking what you might do or say to lead the conversation after the initial hello.Sure, it's not the most natural, but if having something ready to say helps get you into a few conversations, you'll start to relax and it won't be a big deal.