how to completely dry up breastmilk supply

I haven't nursed in 2 months and I don't leak or have any type of real supply anymore BUT I'm wanting to get my nipples peirced and if I squeeze them little droplets still come out. is there a way to dry it up 100%. I'm already a super shy person and am dreading showing my breasts to a person other than my husband. I've just always secretly really wanted them peirced and my husband hopped right on board so I'm doing it but I would rather them not pop out BM drops during the process lol