To be honest, I don't know if deleting songs from your iPod will remove them from the playlists stored there. But as long as they exist in iTunes, you should be able to add them back.
If you want to keep only part of your iTunes library on your iPod to save space, in iTunes, go to Edit, Preferences, Devices, and check the box next to "Prevent iPods, iPhones, and iPads from syncing automatically". With your iPod connected, click on the iPod's icon in the top of the left column, just under the Account tab. In the Options window, check the box next to "Manually manage music and videos".
Now you can add only the Playlists or Music you want to your iPod but keep your entire library in iTunes. Be sure to back up your Library somewhere else as well 😉.