What items will the goriya by the shore accept in exchange for the boomerang?

Solution 1:

First off, your shovel is unique. You can't go get another one. That said, by the time you can get the Boomerang, you probably don't have much more need of the Shovel. And you can always go back and swap if you do. The other items you can trade, by contrast, are far more useful and valuable to you. He'll take nearly anything though, so if you really feel like giving up your Hookshot instead, go for it.

The only items he won't accept are Bombs, the Bow, Magic Powder, Shields or a Power Bracelet.

Solution 2:

The idea is to get all Secret Seashells first (the ones you have to dig up anyway). there's 27 in total, IIRC.

After digging them all up there's no more point to keeping the shovel. The boomerang is one-hit-kill for most common enemies, and also lets you cut several bushes at a time. It is superior in every way.