Swimming is undoubtedly the best exercise for amputees. There are many reason why I make such a claim.
The first and foremost reason is that most amputees can technically swim if they choose to practice & learn. Even if you have a double amputation, below elbow or below knees, you should be able to swim. It will definitely be an uphill battle, if you need to learn, but it is possible.
The second most important reason is the nature of the exercise. It is a non impact exercise, so your chances of injuring yourself and quite minimal. As long as you take recommended precaution under water, you should be ok.
The third reason is that water is calming in nature. For most people who chose to swim, the experience is very close to meditation. Under water, you actually get away from the noise. Your are in prone position, with a reduced gravitational force due to buoyancy, so your heart rate is stabilized. This causes nerves to relax and therefore helps amputees reduce phantom pain or residual limb pain.
Although swimming is considered an aerobic exercise, it also provides strength training due to the resistance in water. And is provides a full body workout. Your breathing is controlled, just like pranayama, thereby increasing your lung capacity.
On a personal note, I’ve noticed, that I get the best sleep after a good swimming session.