Barrel Clips for Fender Emblems

To be more specific, if I cut off the plastic, the metal stud is 1/8" and I'm sure I can use a barrel nut for 1/8" stud. What I'm asking is, if I leave that plastic on there, should I use a 3/16" barrel nut or is that plastic sheath supposed to deform and make the 1/8" barrel nut fit more snugly?

Perhaps you're right and these plastic bits weren't designed for barrel nuts, if so I can remove and use the 1/8" barrel nut.