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I'm getting a dozen WG soon and I want to do something unique with them (because I just cannot bring myself to put together a kit following the GW instructions)

So I am going to mount the gun underslung on the left arm, leaving the right arm/hand free to carry a weapon.
But what will look cooler? A single Sword, or the axe?

Hmm, interesting!
So you will carve the guns from the gun arm and use the melee weapon arms instead. The hands are part of the sword and axe bits, there are no open, pointing or anything but gripping hands for that reason. Maybe you can do something with the hands from the arms that are meant to support the gun.

That being said, I'd prefer the sword and look into incorporating the shield that is supposed to go on the left forewarm when equipping the model with the axe.

yeah, I was thinking of using the melee arms for left and right.
The shield arm would work just fine to the gun to attach. I would cut away the right arm and left hand from the gun, then not us the shield at all and attach the gun underslung where the shield would.
Or I could place the gun under the shield depending on what looks good.

Another option I though about is to attach the gun at the elbow in the same way the Revenant Titan has its guns, but I think I want these guys to match the Wraithlord/Wraith knight aesthetic more.

I am now leaning towards the sword option. It matches the Wraithbone fists profile a bit better than the axe too. And my WK and WLs have swords, so there is that as well