Do I have a 15-002 balance shoe?

I'm afraid that's not a detail that we can eyeball. The only way to determine if you have the 15-002 is to measure it as carefully as you can to confirm if the dimensions match up.

I can tell you that you either have the 15-002, which is 1" deep, or the 15-001, which is 1-1/8" deep. The best way to measure the depth is to stand the balance straight up, like how it looks while installed. Then pretend that this fitting is a foot or shoe. You want to measure heel-to-toe.

When measuring, make sure to account for wear. What I mean by that is that the depth may be a little less than it once was. There's no secret trick to this, you just have to use your best judgement. For example, if the depth of the shoe is more than 1" but less than 1-1/8", then you can logically surmise that it was once 1-1/8" but wore down over time from use.