Well, in the PFH, the monkey was weilding a quarterstaff. And, technically it isn't allowed.
Now, to me - the quarterstaff is the quintessential monk weapon,and mayhaps Larian made that weapon specifically allowed, but I suspect its to do with proficiencies.
So, a Dwarf Monk could still pick up a Battleaxe and swing it. However. That doesn't mean he uses Dex for it. Nothing indicates that. They use Dex for Finesse weapons. That's it. Just like a rogue. A Dwarven Rogue can use a Battleaxe, but not for sneak attack, and use STR for the attacks and damage.
