[mothered]

With the apple watch EB, what would you do with the strap? as the strap and watch come separately inside the box. If one was SE'ing with the intention of selling it, would you just claim EB for the watch component part and sell that on it's own or buy a strap for it?

There's no need to purchase a strap.

Given you're claiming the watch Itself Is missing, It'll be replaced while you still get to keep the strap.