The Way We War

[Morthoron]

In regards to Dain's folk...

In battle they wielded heavy two-handed mattocks; but each of them had also a short broad sword at his side and a roundshield at his back.

Tolkien never claimed all dwarves used axes, or even used them generally in battle, that is an accretion piled on Tolkien lore from elsewhere (like dwarves speaking in a Scot's accent, laddie). Mattocks are a miner's tool, and would be readily available to any dwarf (axes not being of much use in the type of subterranean manses dwarves engineered). Also, there is a tradition of dwarvish sword-making that goes back to Telchar of Nogrod.