It's important to point out that strength training is a better form of fat loss than "cardio".
Beyond that, taking in less calories is vastly easier then "burning" them. To make that clear, the average bagel has 250 calories, which is the rough equivalent of 50 minutes of walking (180lb person, 3mph pace). I mean seriously, which is easier to do: walk an hour or not eat a bagel?
For anyone looking to lose weight, the priorities go:
- Diet. Less calories in than needed.
- Strength training. As referenced in the study above, boosting your basal metabolic rate is far more relevant for anyone but the most active of endurance athletes.
- Aerobic activity, aka "cardio".
In your case, I'd focus on getting your diet locked in. That will lower your body weight which in turn will make life easier on you to move around. With your doctor, start looking into body weight training (including yoga) and go from there.