I’m no “small tin expert”, but based on my own casual research over the years, what might foot the bill for your use is what they called in the 17th thru 18th centuries a “patch box”.
It’s not what one might think, being rifle gunne shooters like we are, but a small round container that held cosmetic “patches or “spots” used by both men and women to apply to one’s cheeks (or in the case of women exclusively—to her bosoms) supposed to enhance one’s attractiveness and/or youth.
These patch boxes look very similar, in size and shape, to 19th century cap boxes.
However I have not found any examples made with tinplate. I’m not stating they didn’t exist, but I have not seen any documentation or surviving examples made of tin.
There are original examples made of silver, copper and brass, or combinations of the latter.
It is well documented that people of the time repurposed containers for other use, I.e. I recall a “lost and found” advertisement for a found mourning ring in a snuff box and anyone claiming to be the owner would have to identify the touchmarks on the box plus fee for printing costs, etc.
While patches and spots fell out of favor toward the end of the 18th century, especially with the growing middle class, the boxes continued to be produced/reused.
Goose Bay workshops (Peter Goebbel) makes these types of boxes, though he just calls them “tiny boxes” or some such.
http://www.goosebay-workshops.com/Boxes-Barrels-and-ContainersRegards
Johnny