Oh upper body strength is very important, no argument there. It is necessary to compensate for a weaker lower half, for sure (and a good thing to have even if your lower half is strong).
It's not that I'd be totally helpless if I had to hit someone with a cane--it would just require very specific circumstances for it to work in my favor. I'd need time to widen my stance, I'd need to have something behind me so that it would be harder to knock me down, and I'd need to be ready to swing the cane while maintaining my balance, managing my fear, and hoping that one or two strikes with basically no footwork would do the job. If any of that is out of place, my odds are really not very good.
I see the appeal of the cane; I would just probably see it more if my body worked properly to where I didn't need it. But, I might just as easily feel secure without any weapon or improvised weapon, too. I've never lived like that so I can't really say, I might think completely different about self-defense, honestly. In any case, I wish you well in your endeavors.
I don't pretend to be in your shoe. It's obvious that you like to learn self defense, or else you won't be hanging around here with old foggies like us. You still in your 30s!!!
That said, too bad life is not fair, you dealt with a bad hand. I don't pretend to know how you feel. One think I know is if one want something bad, there is always a way, it just takes more determination. I have a little of this. When I was in the early 30s, I was so into TKD I worked very hard. My back gave out on me after 3 years from all the high kicks. I really pushed myself. For two years, I could not stand for 2 minutes without the tinkling all the way down to my foot. I was disabled. I did not give up. The doctor put me on PT with weight, that literally saved my life. I slowly work my way back, working on heavy bags and all that. It's been over 30 years, I never stop.
My point is there's will, there's a way. Now I talk about it. But when i was fighting through it, I don't even want to talk, I just do. If you really want it, I don't know of any reason why you cannot start doing weights on your upper body. I don't know your condition and I am not a doctor. If you really want to improve you lower body, talk to the doctor, tell the doctor you want to strengthen your legs, ask whether you can get into PT with weight training on your lower body.
I am not going to paint a pretty picture, you might never get back to like a normal person even if you work hard on strength training on your lower body. BUT at least if you get stronger, that would help. It will open up more option. If you have the determination, talk to your doctor.
Hell, if you can get very strong on you upper body, if you get a 17" arm, people will think twice before picking on you!!! If you are strong enough, you can use two cane, one on your left hand to be on the ground like a 3rd leg to help with your two legs, the right hand swing the cane for defense and fight. design the two cane so they can be held together as one piece so you only have one cane(combined of two) to walk. Separate them for fighting so you have 3 legs and one hand to fight.
I am not saying this is the answer. You have the will, think of ways to make it work. Just keep thinking and come up with solution.
This is what I am doing. Because of my back, I have to think of different ways, not just follow on style because it won't work. Think outside of the box to fit my particular strong and weak point. BE CREATIVE.
One think I do every morning before I even get out of the bed. I just lie there and THINK, just think of possible solution in everything facing me. Not just MA, but other things. I was an EE, you don't know how many ideas I came up with from lying in bed. I had a big bout with back problem just a month or so ago, nothing I did before helped. I came up with totally new exercise just from lying in bed and I am up and exercise again.
Have the determination, THINK out of the box if you really want it. Do something about it.