OK, so I'm overhauling my first 21st century hub, a rear Shimano FH-M525 that I bought used. I loosened the locknut on the NDS, but in the process of unscrewing that and the NDS cone, I found that the DS locknut was loose as well. Now that I've got the axle out (see photo), I'd like to tighten the DS cone/locknut in place after I clean everything, but I'm not sure how to do it.

The problem: the flats on the cone are partially overlapped by the rim of the dust cap when the locknut is tightened. The accessible flat thickness is then only about half(!) the thickness of my cone wrenches (el cheapo Sette brand). Do I need to buy some super-thin 21st century cone wrench to tighten the DS locknut here, or is there some trick I don't know?