Yes, but "power weapons" are non-specific. Here's the power weapon description I'm reading:
Kharn's weapon has a bunch of special rules, so they specified it. But the rest seem to apply the "look at the model" rule, which is a nerf for Dante.If a model's war gear says it has a power weapon which has no further special rules, look at the model to tell which type of power weapon it has: if it's a sword or dagger, it's a power sword; if it's an axe or halberd, it's a power axe, if it's a blunt weapon like a mace or a staff, it's a power maul, if it's a spear or lance, it's a power lance.
Unless you're saying that since it has "master crafted" it has further special rules, then we're stuck with it being a "power weapon" and don't have any indication what type of weapon it is.