I bought some of the shotshell kits from H&C here: https://www.hc-collection.com/calibre-16-broche-de-chasse-c102x333683
I have ordered many things from here to the US fine and they always arrive with no issue.
Since it is coming from France you will have to source your own black powder percussion caps, but you can get those anywhere. The hardest thing for me was actually finding small round toothpicks that fit in the case to hold everything down!
Here is what everything broke down to shipping it here:
That is about $20 each with plenty of extra pins and wads for loading many times. The benefit of these is that they can be cleaned and reloaded relatively easily.
Another option is buying original period 16g NPE shotshells. I have loaded many myself and sold hundreds to others and the vast majority go off fine even though they are over 100 years old.
Here is what those metallic ones look like loaded:
And here is what they look like after being shot (along with some original period ones I shot in another gun):
And here is the outcome after a couple shots:
And Here is a video of me shooting it!