No, you don't have to climb stairs but would suggest you go to your muster station about 15 minutes ahead of time so you're not jammed in the elevators ... same thing after muster - wait a bit. And, you do NOT have to go out to the lifeboats on Princess and stand in the hot sun.
I cruise the Emerald Princess, Eastern Caribbean on April 16, 2012
CruzNut is absolutely correct. CP has the most painless muster drill of any of the lines! Depending of where your cabin is, it will be in one of the lounges, or the theatre. If I were you, I'd go to your muster station early, and that way you won't have to use the stairs, or explain why you can't. It will involve your sitting just a bit longer. Once there, explain your physical problem to the ships crew member , and I'm sure they will take care of you.
Why is it called "Muster Drill"? Muster, simply means "to assemble, or get together in one pace". Therefor the "Muster Drill" is just that. Practice get together.
During the drill you should be advised to let your cabin steward know if you have mobility issues & they will make arrangements in the case of an emergency - presumably using alternative exits & evac-chairs which are brilliant.
The reason that you are advised not to use the elevators is that power may be cut to them, so it is better to let the trained staff look after you.
Hope you have a fantastic cruise, Princess are by far our favorite cruise line, and I'm sure they will do everything they can to make your vacation memorable.
Alan & Katrina
Last Cruise: Queen Victoria November 2014
The word "muster" means to assemble for inspection or to give orders.
It is true that some people have been known to mistakenly go to the Gulden's dispenser at the outdoor grill on the pool deck, but it isn't a "mustard" drill.
If you tell your cabin steward as soon as you board that you have a temporary disability, they will make sure to get you to your muster station early by elevator. This is very important, because the crew needs to know about your inability to do stairs in case there's a real emergency. They must have it on file that they need to come get you. So this notification serves that purpose as well.