I actually bought my last bunch at Academy about 5 years ago, 9mm, 45apc, & 380s. The brand isn’t on the caps. They are the typical red plastic with a spring attached to where the primer would be. I haven’t had one break but I lose the damn things over the years or more likely, one of my adult sons ended up with them.
To answer your question, I do not know the exact SAE size of mine.

Based on my recent bad experience with snap caps at the range How long has it been since you've been to the range? - #803 by Gary_H , I am thinking of making my own.

All of my SD ammo is nickel plated, so I’m thinking crimp a bullet into a fired brass casing. My mental debate is whether to push the spent primmer out and let the firing pin hit air, or leave the spent primmer in and let the firing pin hit it. If I leave the spent primmer in, then I will definitely drill some holes in the side of the casing to positively identify it. Any thoughts?

Push out the primer and fill the hole with silicon, rubber or plastic.

I would avoid drilling anything in the side of the casing.
To make your dummies easy to recognize, I would paint projectiles in yellow or orange.
(do not use red, unfortunately Federal uses this color for live ammo)