To really do this question justice, one has to research the mime's way of life. So, I took it upon myself to study the writings of Brian P. Cleary. His revolutionary book 'A Lime, A Mime, A Pool of Slime' has transformed the way mimes and the miming artform are looked at throughout the entire world.
Now take for example the Mahāyāna Buddhist Zen saying "If a tree falls in the woods does it make a sound?"
and if we apply that to mimes, we should ask "If a mime performs miming in the woods, does he/she make a sound?"
One could say "well it depends on how good his or her skills are!" or "What if they stepped on a twig?" or even "what if they're sick with a bad cough!?"
but we can't factor in a mime's health to solve this question. we know mimes are in top physical condition, far beyond the health of regular athletes such as Olympians.
The flabbiest and most out of shape male mime having a body type like this:
and the most flabby out of shape body type for a female mime has been reported as this:
Alright, so now that we know that there aren't any other factors to consider such as illness or lack of sk... WHAT? you're telling me that second one isn't a girl? That's Carrot Top the prop using comedian? Well what the hell are his props now? Steroids?
anyway as I was saying, the only logical answer to the question of whether or not they make a sound is No. They don't. Mimes live on a metaphysical plane of existence which is a state of consciousness that transcends the known physical universe. Because of this, they're physically incapable of creating or for that matter even hearing sound. Their existence in our physical universe is limited to vision, miming and coin gathering.
So to answer your question about whether or not I'd use a silencer, no I would not, because they wouldn't hear it anyway. Of course, I would never shoot a mime either, because as you can see from the weakest of their specimens, bullets wouldn't have any effect on them anyway, it would probably only make them stronger.