I can't see an immediate decrease in strength occurring, assuming you don't get the thing red hot. You're actually increasing the amount of material at the face for a slender nut.
It will rust, however, and potentially cause the rest of the plating to flake, as mentioned before. They'll also be more likely to damage painted items as you use them.
My thought process, however, is that the 'slender' nuts you're turning probably don't need a lot of torque. Why potentially compromise one of your good sockets for a higher torque application? Can you grind a cheap socket or socket set down and meet your needs?