Bandages make me think of attacks like Wrap and Bind.
Has to use his arms and such to battle, so as a physical Fighter, it needs Karate Chop, Close Combat, Brick Break, Rock Smash, Drain Punch, Vital Throw, Revenge, and Focus Punch.
As for physical Ghost attacks, Shadow Sneak and Shadow Punch should be enough (doesn't seem to have claws for Shadow Claw).
For special STAB, Aura Sphere, Shadow Ball, Focus Blast, and Vacuum Wave should be on it.
It's a mummy, so Sand Attack, Mud Slap, Mud Shot, and Earth Power to make it unique from the other Ghosts as well.
For other kinds of attacks, U-Turn, Body Slam, Ice Punch, Knock Off, Facade, and Rock Tomb seem to work well for it.
And for other stat changing/status abilities, I like Glare, Nasty Plot, Bulk Up, and Sing.
The reason I didn't add things like Ice Beam, Energy Ball, Thunderbolt, Dark Pulse, or other common special attacks is because those are typical special attacks Ghosts learn, and since this thing is part Fighting and most Fighters don't have access to moves like those, that limit should be in place; that's the same reason I didn't give it Rock Slide, Stone Edge, Cross Chop, or Earthquake, as Ghosts don't learn those attacks either. I think that the mummy should play off of the fact that it's a hybrid of those types instead of capitalising on it being one or the other, as it seems that most people are focusing on it being a Ghost when it comes to all of its attacks, and focus only on the Fighting for STAB, Rock Slide, and Earthquake.
Also, Pursuit and Sucker Punch are attacks that Dusknoir, Banette, and Spiritomb need to be somewhat different from the other Ghosts, so I didn't feel that the mummy should take anything more away from either of them.