Other than finding them and giving them to Shinwa, are we able to use them for anything else, like assembling them to make a bracelet, or something else?

I don't believe so

put them in a pet's Treasure Chest, sell them to other players who forgot that they ran out of one of the quests that she asked for?

If only the 5 shards can be assembled into a Shinwa Strength Bracelet :D No, they are just quest items, or hoarder gallery fodder on top of what said.