Based on the information here and the information about your wife's knees having a low amount of cartilage, you want to avoid motions that require the knee to bend--particularly under weight.
At first I was going to suggest weight training, as you are very controlled about the weight that you apply and it can strengthen the muscles and ligaments surrounding the bone. It is much lower impact than running which can place 2-3 times body weight force on the knee. With weight training it will be several years before your wife could possibly work up to those weights. The strength would help in controlling and minimizing the forces that you have to deal with in skiing. Squats, the king of all lifts, would be the best lift to support skiing in general as all the muscles and joints affected by skiing are strengthened with this lift. The problem is the medical condition where this may not be the best idea. At the very least, run it by your doctor explaining that the motion is slow and controlled, and that you won't be putting a lot of weight on there. If you do choose to incorporate these, I would start with just the bar, and increase by no more than 5 lbs at a time.
However, considering that the only way for cartilage to begin healing itself is to stop any activity that would wear it away faster than it can be rebuilt, I'm thinking that swimming might be a better option. Swimming doesn't have the impact problems as running does. If you choose a stroke that uses a scissor kick to prevent movement in the knee (which will potentially wear away cartilage), that can provide enough resistance to strengthen the leg without the negative problems of wearing away the cartilage. The idea is to minimize the movement of bone on bone as much as possible. That's why I think this might be better received by your doctor.
Keep in mind that skiing can present a lot of force to the knee. In the case of skiing moguls or doing any sort of jump, I would not be surprised if the forces presented to the knee are greater than that from running. Please do be careful.