I see that the Norwegian Sun has a wifi hot spot. If I take my laptop on an Alaska cruise and use the hotspot, making it obvious to all and sundry that I have a laptop, will it be safe in my stateroom during shore excursions? Leave it with the purser?

I can't speak for NCL but we've taken our laptop on several Regent cruises and this was never a concern. The only person who may be entering your cabin while you're away is your room steward/stewardess or a butler if you have one. Such a concern never crossed my mind. I wouldn't worry about this.

Just don't leave it out in plain sight in your cabin. You can lock it in your suitcase or hide it between the mattress and the box spring. Bury it somewhere.

Do you travel with your laptop to hotels? Seems this is not really different than that. I think putting it out of sight in your cabin is a reasonable precaution, but perhaps not in bedding since this would interfere with making bed up by cabin staff. I doubt people would be casing WiFi zone and then stalking you to steal your laptop, but that is just my opinion. We all have our own things we worry about - this just isn't one of mine.

I work in a hotel, where guests' personal items occasionally disappear.

In a hotel, if an item is not in a safe, there is a law protecting the hotel from liability. I would imagine that a ship is somewhat the same. You would bring your laptop along at your own risk.

We too have brought a laptop and used hardwire inside our cabin (wasn't NCL ship). Never put it away, sat on our desk all the time. Never occured to us to hide it from our room stewardess. I think the room steardess/stewards on cruise ships are very honest.