I live in the woods and have both. Not sure about Shrews, I have only found dead ones that something has gotten. Chippers on the other hand WILL dig tunnels and often under plants. They help me transplant things now and then. Why would you trap them? Are Hostas more important than a little furry creature? Deer eat Hostas. We are not talking mice or rats here. Let them be. The Hawks will keep their numbers under controll as will neighborhood cats etc.

Christine,
I don't personally condone trapping anything.
It's unfortunate that it's even in anyone's vocabulary, unless you are a fur trapper...in which case you're about 150 years too late.
Some gardeners can be such hypocrites.
"I love nature....as long as it obeys my terms."
Learn to adapt to and appreciate the native species around you.

Anyways, my preaching aside, I have chipmunks and hostas and they coexist peacefully. The chipmunks do burrow in a few places, but that's what chipmunks do. I would be surprised if they are your hosta munchers though.
As for the shrews, they have voracious appetites and many also burrow, but I don't know if hostas are on the menu or not. However, they are not rodents (not even closely related) and are actually relatively intelligent species for their size.
I say live and let live. Maybe find out which hostas are getting eaten and which aren't and try to figure out why. Or look at it this way. You have apparently created a great wildlife habitat. Good for you.

And before there is a backlash of posts advocating trapping, let me just say that unless there is a large, unchecked population of potentially dangerous or destructive animals on your property, then no, trapping is not cool.

Shrews eat insects.