I'd start with 0.005" styrene (Evergreen) or brass, as 0.01" would probably be too thick. If it isn't enough, you can always try thicker stuff. If 0.005 is too thick, and the coupler binds, I have no idea where to buy thinner brass, although I know they used to sell it in some hobby shops.
On a McHenry coupler, you could also try bending the shank, but I'm afraid it would break rather than bend.