The Way We War

[Kuruharan]

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).

I'm not sure I agree with that. I think we do have evidence that Tolkien thought of the axe as being the primary dwarven weapon.

Gimli used an axe (obviously). Thorin used an axe at the Battle of Five Armies and Azanulbizar. When speaking of Thorin's condition in exile Tolkien used the phrase "the axes of his people were few." The dwarves whalloped Glaurung with "their great axes."

I can't recall any good example from the Middle Ages now, but for example among the ancient Israeli warriors there has been a caste of special fighters trained to fight left-handedly, or such, you have all sorts of special groups of warriors trained to fight with some unusual weapon or in some unusual style throughout the cultures and times, so perhaps the Dwarven axemen were something of that sort, too?

It is an interesting theory. I'm not sure its one I can agree with, but it is interesting.

Is there any evidence that the Dwarves used distance weapons of any kind? Bows, javelins, catapult, trebuchet, slingshot, whatever?

Thorin used a bow that just happeend to be lying around (implying that the dwarves kept stockpiles of them to use) to shoot at the messenger. The dwarves did use (without much success) the bows Beorn gave them...which I think has largely led to the stereotype that dwarves can't use bows effectively.

Slings would be an interesting weapon for dwarves to use if they were incapable of using a bow effectively, but I don't think there is a single example in Tolkien of a sling being used.