Controlled breathing, as mentioned, is central to the wim hof method, the yogic practice of pranayama, and to many kinds of martial arts and meditation, and doesn't really have the potential for injury (with the exclusion of the more physically demanding martial arts). Some of those practices are also more accessible to people with mobility issues.
My personal experience with yoga and meditation, is a very significant uplift in mood, and better sleep (I used to have a very bad snoring problem). I also do a mix of weighted exercise, callisthenics, and cardio, and I've found the combination to work very well.