Seems a lot here are not reading what the OP is saying ?
He will have NO ammo legally on the flight in or out, so no permits & no box to put them into.
In this day & age, if you want to lessen any problems check all rules Airline & Countries you are leaving & returning to, as laws change over night.
Empty cases fired or not are treated by lots of law enforcement & government agencies as ammunition components (as they should really) no amount of sweet talking can change laws/rules & you could be charged with a offence or at the very least miss all your flights & feel Very uncomfortable !
Posting ammunition components can also be a legal problem.
Now I was arrested & had a horrible time for having FIRED Spent bullets/projectiles that were dug out/found in some of our animals, these were in checked baggage, not in my pocket or such !!!
You can argue all you want that those projectiles are useless pieces of metal & could never be loaded into a cartridge case but the fact remains they are ammunition components & the law may say that is illegal without correct permits to export or import, a lot of travelers, Americans are the biggest culprit here as they have so many freedoms in the USA, think it’s ok to do this or that as it’s Ok or cool in their countries or worse 10 other people or friends have done it, well probably lots of Heroine or Cocaine smugglers don’t get caught either ?
Still not legal & it’s a gamble with anything firearm or even weapon related, ie knives sprays, one handed opening knives, double edged lots of stuff !
I know hunters arrested for ivory smuggling in cells for a long time waiting justice that had undeclared Warthog tusks, obviously not real ivory & not a problem, tell them that, lives destroyed & hours or days of terror.
When it happened to me there were a couple of American hunters Bryan Hagerich & Ryan Watson awaiting trail for some months or longer on bail in the Turks & Caicos evidently had spent cases in they possession, a common offence so it was said & normally a small fine but not this time !