Some Vape shops carry various kinds of steel mesh.
If there are a few in your area, you should be able to walk in and check out the screens by hand to make sure its what you're looking for.
Call ahead first, because not all of them have them... using steel mesh is kind of a new thing I think.
I've seen the bulk mesh screens for the do-it-yourselfers, and also little steel screen caps made to fit into a vaping tank. Those little caps would fit perfectly into a cut circle, or into the end of some tubing.
These vape shops also tend to carry 100% organic and unprocessed cotton.
And, if they mix their own juice, they should have either medical or industrial syringes...though they may have a policy to not sell those.