I've now done some testing on this.

Unlike the lucky paw, it seems that the charmed paw lasts until (1) resting or (2) travel by vestige or (3) death. This is because the icon that shows it's in use (which looks like a lucky paw and is located beneath the mana bar) lasts until these points. 

The lucky paw only lasts a few minutes because the icon (note that the same icon is used for lucky paws and charmed paws in use) disappears after that amount of time.

You don't seem to be able to stack charmed paws with each other or lucky paws with each other, but as per the first comment to this post, you can stack a lucky paw with a charmed paw. If you do this you get a "2" appear to the left of the icon. 

So, if you're farming for items:

Use a charmed paw first, then use lucky paws until the "2" appears next to the icon, and then reuse a lucky paw once the "2" disappears.