Just going from the O.D. you provided here's a link to the McMaster list of SAE and metric locknuts.

https://www.mcmaster.com/products/sp...bearing-nuts~/

Looks like the closest SAE would be a N-06 nut. And the metric would be M-26 or M-30 depending if the face is stepped or chamfered.

The spanner sockets are also listed to the far right on the chart. That chisel method is looking way more economic. Don't be afraid of using the chisel I've used that method of loosening and tightening spindle nuts for 30 years.