apple watch

Just before you place the watch only in the box make sure you have followed this: What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support and take good pictures of the watch from all angles and take a video of it working then put it in the box and ship it.

If you're trading it in with Apple then no, you do not need to send the watch band. Just the watch itself.