I'm reading mixed terminology here...
Air-mix screw and "pin"... I assume they are the same thing...
You can buy a new one easily... but,.. you do have to get the old one out...
1. you don't want to booger the threads...
2. you are working with brass and aluminum... both are very soft... (an extractor will eat through very fast)..
I'd take a careful, careful look at the surface shape of the screw... Use a strong light and a magnifying glass... see if you can find a surface irregularity to take advantage of...
Grind or file a small, flat blade, screwdriver to a sharp tip, with sharp edges.... and try to cut it into the screw head... (taking advantage of any irregularity you found)...(if you didn't find any.. make one)...
This screwdriver is a throw-away... (but, I never throw them away... may need one again)...
Try to tap it into the screw... (steel will cut brass)... with a small hammer... then, if you can gain some bite, you can unscrew it...
...(lube the mix screw up good with penetrating oil, first)...
Sacrifice the screwdriver,... and the screw... but don't hurt the carb body...
JMHO... this is a vague description of how I usually tackle similar problems... (others may have better advice, for your particular situation)...
Mostly... don't tackle a tough situation, with brute force...
Be calm, slow, and patient...
It's when you get frustrated that you will booger things up...
Best luck...
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