Just measure the nut, much easier
Use a 6 sided cylinder and measure across the points for the cylinder diameter.
How did you glue it together ?
Otherwise not sure it'll last past the first throw.
If you embed and glue the nut fully in one side and add some threads to the other side and use something like polyurethane, that would be pretty durable.
Or thread both sides for a centrally mounted nut.
Oh and I'll add the sling-,in-the-dark ammo here as well