The OP wanted to know what size nipples to use for a replacement!

Just get nipples for 14 gauge spokes.
A 14G spoke should have a 2mm diameter or about .079".
It's unlikely the threaded ends are anything other than 14G. Possible, but unlikely.

Although it's 56 TPI, I doubt it's a 2-56 thread, whose major thread diameters vary between .813 to .854.