those missile coolers are pretty small, but their not cold enough.
I imagine it would need a moisture scrubber. But if the point is to make 1 drop of liquid air every say 15 seconds, I don't think thats a particular hazard....
So in addition to a adamantium compressor, you need some kind of micro nitrogen separator membrane, so you blow a stream of nitrogen over the tip like a tig torch shield.
Hopefully we can buy these in 5000 years, powered by 2 AA alkaline cells and sold for $20 by general tools near the engraver and disposable electric screw driver.