In the late middle ages chainmail armor, sword and shield was replaced by plate armor and double handed polearms like halberds, which were essentially long axes with additional spikes for penetrating armor and hooking your opponent. It is likely dwarves underwent a similar transformation due to the very high quality of their armor. A double edged axe however is impractical, you don't need 2 edges that are exactly the same, it is dead weight and rarely is there a situation you need to rapidly strike in the other direction without taking time to turn the weapon around. It could be a ceremonial axe which Gimli took to the meeting at Rivendell, and his decision to join the fellowship was spontaneous and since even ceremonial weapons among the dwarves are expertly crafted it was still useful, if not optimal.

All this speculation is pointless however, most combat in lord of the rings is not historically accurate, even excepting lore accuracy like the gymnastic talent of the elves or the super strength of the dwarves, spinning around and waving their shield around leaving themselves open is just pointless. The best "world building" is when you take reality and add only a few clear changes and make sure everything consistently follows these rules. If you want something zany and exciting to happen in your story, it is lazy to just retcon or deus ex machina it rather than work it into the plot. Though they did put in more effort than most. I liked the Uruk Hai formations at Helm's Deep and the siege engines and different phases of battle instead of just a wild charge as you often see.