Same as Gary said: helmet, mask, dangler, and catcher's mitt. If WR is saying the warmup catcher has to have a cup, there is NO rule stating that.
Now, even with 9, I never had an adult take warmups on the small diamond. EVER.
With 9, the 3b takes his glove and hat along with the catcher's mitt and mask out there. Toss the glove and hat off on the 3b side and take the warmups. When the catcher is ready, the 3b grabs his hat and glove, and the 1b is instructed to give him the next 2 warmup throws. He's had the tosses back to the pitcher anyways, so he won't be 100% cold either.
I look at it as free catcher practice. The coaches who won't put a kid out there are the same ones who complain they don't have enough catchers ! So, MAKE some.
I always had a clipboard with my defensive lineup on it hanging in the dugout. The warmup catcher, and the player responsible for warming up the outfielder were also on it. The KIDS also counted the pitches for me (if I had enough). The pitch counter was also on the defensive lineup as well ! If you have 12 kids, you have 9 in the field, and the other 3 have a specific task to do. NO ONE does nothing.