Hang cleans can be performed in many different ways and that will impact what muscles are being taxed. For example, how high is the hang? Well above knee, at the knee or below knee. How deep are you catching this? Is it a hang power clean (only slight leg bend at catch) or is it a full squat clean catch?
This could be considered primarily a leg exercise. The traps will generally be another large contributor in this movement. I think you could add it to legs, back or shoulder day. If it was on shoulder day it would be at least 3 days away from legs and allow for complete recovery. However, if you do heavy shrugs on back day then you probably don't want it on shoulder day.