I removed the shrew-proofing mesh from my hives yesterday so I could clear out the dead bees that have accumulated so far this winter. I reattached the mesh afterwards with the use of a staple gun that produces a loud bang that vibrates through the hive and riles up the bees. But a suggestion from one of my readers changed everything:
“Would it be possible to secure it [the mesh] with drawing pins rather than staples?”
It’s absolutely possible. I did it today, just five minutes ago.
The drawing pins / pushpins work just as well as staples as far as I can tell. That mesh isn’t going anywhere.

Three green pushpins (instead of staples) used to attach mesh over bottom entrance. (Dec. 13, 2015.)
Now I can easily remove the mesh, clean out the dead bees and reattach the mesh without bothering the bees. I thought I might need to find a different method for keeping the shrews out of my hive for next year. Not anymore. The mesh attached with pushpins instead of staples works perfectly. At least that’s my story for now.
Thanks for the tip, Emily.
December 18th, 2019: I’ve gotten into using regular thumbtacks instead of pushpins because the pushpins can be rather difficult to drive into the wood. A thumb tack is much easier to attach. To remove one, though, requires pulling the mesh off carefully and taking the tack with it, which can then easily go flying into the grass or get bent to the point of not being reusable. Still, they’re so much easier to use than pushpins, I might stick with them. I suppose I could use one of those staple remover things that look like a tiny fanged mouth, but that’s another gadget I’ll need to keep around and I’m more interested in reducing what I need to keep bees instead of adding more to the list.

Thumbs tacks used to attached shrew-proofing mesh. (December 2019.)