Loading 000 buckshot in the .38s is as old as the hills, I think. I think it is 00 that is close to .31 and can be loaded in .30/'06 for shooting mice and rats... Size the shot or bell the case mouth. Couple grains of bullseye. NOT MUCH. And 0000 is close to .375.
GOVERNMENT used to have a .45/70 shot load in a wood capsule--bullet shaped.
I think it is #4 buck that is about .24. You could flatten it a bit to make it work in a .25 anything.
BEWARE. These low pressure loads will not fill the chamber with a case under high/normal pressure. In the case of rimless rounds, they grow shorter as in "excessive headspace" from force of firing primer and can with a successor full load pull apart and cause TROUBLE! DON'T! Belt or rim negates this problem of shortening.
It is fun, but it can be quite dirty. Low pressure and things don't burn cleanly. And you won't have anything worth anything out of the back yard. So how much "mouse hunting" do you want to do in the basement/barn??? Enjoy, luck...