I don't think
you NEED to crush the eggshells, but you might want to so that their benefits are available in your worm bin. The two main reasons people
add crushed eggshells to a worm bin is to make the environment less acidic, and also to act as grit in the worms' guts. Worms don't have jaws and can't bite, so can only take in very tiny particles of anything, including eggshells.
If you don't want to use electricity, an old-fashioned mortar and pestle would probably actually work better. I wish I had one. I use a food processor for just a few minutes, and I feel like it uses very little electric, compared to so many other things I use on a daily basis.
Now I am curious how long an eggshell would take to break down in the bin without crushing. I might add just one to see.