do I need to send in the watch band for a trade-in?

No. For information about sending watch bands with trade-ins, see the following from Apple Trade In - Apple

Do I need to return accessories to get the full trade-in value?

You don’t have to, but you can always send in your chargers, cables, cases, and watch straps and we will recycle them for you.

If it has been less than 14 days, see the 'Exchange an item' section (and others) in:

Returns & Refunds - Shopping Help - Apple