Are you certain it is not just the excess grease hasn't been pushed out of the way from use?
I usually find thin wall sockets at my auto parts store or other tool store.
On the pedals I use, the spindle along with the bearings comes out of the pedal completely. Then you adjust the bearings with what ever you have that fits. In fact, mine have a lock nut to tighten against the nut/bearing cone, so you'll be SOL if that is the case with yours.