No, no. “A cartridge in a pear tree” refers to ammo.
There are many variations of the song across the world and across time:
https://en.wikipedia.org/wiki/The_Twelve_Days_of_Christmas_(song)
My wife has a small tabletop Christmas tree, with a nativity set underneath composed of heavily anthropomorphized bears.
I constructed an inert .357 mag “training round” and hung it in her little tree.
To her credit, she “got it” pretty quickly.