If all you are going to do is paint the calipers, why do you need to remove the axle nuts?
Anyway, find a flat blade screwdriver that fits in the groove. Tap it in, with a hammer, to lift the lip on the nut. Once you get a little clearance with the screwdriver use a small round ended punch to finish lifting the lip. Remember you only need to lift the lip to just clear the groove. If you remove the nut, be sure to re-torque it to the proper amount when you reinstall it. Have someone apply the brakes to keep the axle from turning while you re-torque the nut. That works good for the removal also.