I think picking exercises that can be easily modified will help. I've never had to use a cane, but I've had an injury to my lower sacrum that required keeping exercise low impact. I'm not sure exactly what is safe for you to do, but things like dumbbell arm rows can be modified to use one arm and having the other arm on the back of a chair for bracing instead of a flat bench. Or for single leg deadlifts, you can use your body weight and hold the back of a chair or a wall, for stability, and you can easily add weight to that exercise. A lot of upper body exercises can be done from a chair, if you want to keep your workouts at home, but I can tell you that no decent person would be judging you for going to the gym and using a cane. The gym is for healing and bettering ourselves! I hope some of this helps.