I respectfully disagree.
Using a cane
If you are using a cane because one leg is weak or painful, hold the cane on the opposite side from the weak or painful leg. For example, if your right hip is sore, hold the cane in your left hand.
If you are using the cane for a little help with balance and stability, hold it in the hand you use less. If you are right-handed, you'll probably want to hold the cane in your left hand to leave your right hand free for other things.
https://www.emedicinehealth.com/using_a_cane-health/article_em.htm
Weak or painful is also a way of saying injured. When I shattered my right femur and started walking with a cane after using a walker I used it in my left hand. I was also obviously unable to drive.
Second source:
Cane Basics The most common question about using a cane is, "Which hand should I hold it in?" The answer is the hand opposite the leg that you had surgery on, or that is the weakest.