Protocol for measuring stamina of arthritic mice
I believe the standard is an graded-speed treadmill test.  An example pub:

Genetic variability in forced and voluntary endurance exercise performance in seven inbred mouse strains

If there is a particular ethical concern, you should always have your institutional review panel review it.  If you call up your department of animal resources (or what ever it is called in your institution) they will almost always give lists of preferred LOPs.

Another option would be to score time sleeping if you have them under behavioral surveillance.  The problem with this is the large amount of man hours needed, even watching tapes at high speed.  Instead I recommend you check this paper out:

Evaluation of two automated metrics for analyzing partner preference tests

Then to get accurate scoring, I would put a strongly colored bedding pad in a corner so the computer could pick it up.  Be sure to put the bedding in at least a week before so the mice get used to it and actually sleep on it.