heat up the nut, I used a 150w soldering iron for the job and left the nut on the end for 5min or so, then press it into the middle of a wheel that has been drilled out. 13mm should do the job fine.

The thing you have to watch is that you get the nut in straight. If it's even slightly off then your wheel will wobble.

Once pressed in, I'd use the iron to cover over the nut to keep it captive within the wheel.