It can work if you feed layer feed, but if you feed all flock like many of us do, feeding back eggshells just won't be enough
Let's discuss this a bit. Part of the calcium in eggshells or oyster shells the chicken eats is not digested. It passes straight through the chicken and out of the back end. Also, the chicken needs some calcium for growth or body maintenance. If the only calcium the chicken was getting was from her own eggshells it is a losing proposition. She will have a calcium deficiency.
But that is not the only possible source of calcium. They can get calcium from certain plants they eat. Certain creepy crawlies they eat contain calcium. Things like hard-shelled bugs, mice, frogs, small snakes, crawfish, and snails with a shell. They may eat small rocks like limestone that are high in calcium. And of course chicken feed has some calcium in it. If all they eat is Layer then they will get enough calcium for eggshells from that but if they eat low calcium treats in addition to Layer even that may not be enough. If they are getting enough calcium from other sources then they may not even need the calcium in their eggshells, let alone oyster shells.
The test is to look at the eggs they are laying. If the eggs have hard well-developed shells they are getting enough calcium from some source. If the shells are thin or soft, you need to add more calcium supplement.
I was looking for calcium alternatives for the chickens that weren't oyster shells.
Some critters have two different types of shells. Crabs or crawfish are probably the best to demonstrate this. The soft translucent parts are made of chitin. This is a protein. They might eat it but it is fairly indigestible. Not much calcium or nutrients here.
The hard parts, pincers or parts like clam shells, are calcium. You can use that hard shell like you would oyster shell.
I do not know what is causing that smell. You can get a strong smell any time you are in a marine environment. In your situation I'd feed it to them if they will eat it. But that is just my opinion.