When Mork takes the picture of the young bride and crew, you can see the flash bulb briefly in his hand just after the flash of the "blueky" in the glove of Mork's right hand.
Even if the Orkan Navy allows its Captains to perform marriages (see trivia), logically this power would only apply if they are aboard ship in international waters and/or interplanetary space. Ever since Mork's ship disintegrated on arrival in Pilot (1978) (as shown in each opening montage), he is no longer an active Captain. Even in fiction, the Captain does not have shipboard powers on land. Mindy's attic would be in the jurisdiction of Boulder city laws, regardless of fictional Orkan custom.