DITTO on E6000.

This is what professional jewelers use to attach stones to settings without prongs, and professional crafters who sell their works use to permanently attach anything else together. There are very few materials that E6000 does not attach together.
Hot glue is an absolute joke, in my opinion. It is what gives "crafters" a bad name

as the items fall apart within days to months of making something. "My mom is into 'crafting',"

said as the child is picking up dropped shells off the floor so that their friend does not step on the shells. "Yeah, my mom does that too, and all the stuff falls apart."

Hot glue is for instantaneous satisfaction, not PERMANENCY. Projects can be glued together and
completed in 2 hours -- never mind they will fall apart and continue to fall apart in the next few week to months until the project ends up in the trash.

At least a non-crafter
completed a project and can be proud for a couple weeks. That seems the goal of "hot glue crafts," from what I can tell.
Hot glue is a non-sticky stick in it's usual cold form. One heats it and AS IT IS HOT is sticky. If one doesn't embed the attachment securely INTO the hot glue and have the glue come up and AROUND like prongs or a bezel to hold the item into place, once the glue is cold again, it becomes NON-STICKY again, meaning nothing else about the glue holds the item into place. Also, if one places the item in a hot place, like a really sunny window, or direct sunlight, the glue may become warm again, where the prongs/bezels holding the items into place melt and the attachments fall off. And since most hot glues remain a little flexible, if one knocks into an attachment, one may knock it off.
If (general) you are going to the effort to take a couple hours to assemble and glue a craft, then make the effort to buy the right adhesive to make it PERMANENT. I agree with using E6000 and a toothpick to dot on the E6000 to the backs of the shells, so you don't smear it all over your hands. Make sure your area is ventilated. (Keep a window open.

) It will take about 24 hours to cure, instead of a quick 2 hours with hot glue. Yet your frame or box cover will be permanent.

The shells, themselves are still fragile. But where they've been glued on, will be strong & permanent.
(Can you tell I have an intense loathing and contempt for hot glue?

)