It's his candy shop. If he says Dwarves primarily fight with axes, despite telling as many stories of dwarves who don't as who do, I'm prepared to believe him.
Meanwhile, here are a few more Dwarven axe references to balance the other weapons you've noticed.
And the eastern host of the Orcs was taken between the armies of the Eldar, north of the Andram and midway between Aros and Gelion, and there they were utterly defeated, and those that fled north from the great slaughter were waylaid by the axes of the Naugrim that issued from Mount Dolmed: few indeed returned to Angband. (Sil, 10, "Of the Sindar")
Glaurung and his brood would have withered all that was left of the Noldor. But the Naugrim made a circle about him when he assailed them, and even his mighty armour was not full proof against the blows of their great axes; (Sil, 20, "Of the Fifth Battle: Nirnaeth Arnoediad")
[the dwarf] Mîm was old even in the reckoning of Dwarves, old and forgotten. And in his halls the smithies were idle, and the axes rusted... (Sil,
21, "Of Turin Turambar")
Behind [Smaug] where the walls were nearest could dimly be seen coats of mail, helms and axes, ... (Hobbit, XII, "Inside Information")
Now the dwarves took down mail and weapons from the walls, and armed themselves. Royal indeed did Thorin look, clad in a coat of gold-plated rings, with a silver hafted axe in a belt crusted with scarlet stones. (Hobbit, XIII, "Not at Home")
Thorin wielded his axe with mighty strokes, and nothing seemed to harm him. (Hobbit, XVII, "The Clouds Burst")
`Well, I can read no more for a long way,' said Gandalf, 'except the word "gold", and "Durin's Axe" and something "helm". (LotR, II, 5, "The Bridge of Khazad-dum")
[Thorin] thought of weapons and armies and alliances, as his great hammer rang in his forge; but the armies were dispersed and the alliances broken and the axes of his people were few; (LotR, Appendices, "Durin's Folk")
...the battle-cry which [Gimli] uttered in the siege of the Hornburg. That at least was not secret, and had been heard on many a field since the world was young. Baruk Khazâd! Khazâd ai-mênu! 'Axes of the Dwarves! The Dwarves are upon you!' (LotR, Appendices, "The Languages and Peoples of the Third Age")