Gogo... you have to remember that he is not going to "learn" or "remember" that he can't walk as well as he always did. It is just beyond his abilities at this point. Showing him a video of himself will not accomplish what you want. He will either say it is a trick, get upset or embarrassed, or not even recognize it is him in the video. Even if you got through to him in the moment, he would forget it before you had the equipment packed up!
The cane or walker are new to him. New equals learning and learning is beyond his abilities. Rather than being a benefit they are a hindrance and potential danger. At best he would just forget it was his and walk off without it. Yes, at one time he was a strong/fit physically balanced man. Now he has a disease that prevents him from being what he was. Think of it as a broken leg. You would not ask him to walk as he did before if the legs were broken. The bone is intact but the ability to use them effectively is broken so it has the same result.
What type of bed does he have? Is it possible to get a lower bed? This might alleviate his anxiety about sleeping in the bed. Perhaps rearranging the furniture in the room would help. Putting the bed where the couch is now? If he is in a double bed, you might want to try a single bed. Then again, if he is sleeping well on the couch then let it be.
Yep, the fall risk stage can be nerve wracking. Dad was bad to fall. He thought he could walk... oh heck he could run! He would get up (after numerous attempts), get a few steps, and plop. If we were lucky he would fall back in the chair or bed before he got two steps. That is why we went with the chair/bed alarm. The staff was great at immediate response to that alarm. But yet he still fell from time to time.
As far as walking with him, make sure he has a belt on. If he doesn't wear a belt ask the physical therapist if you can get a gait belt. It's just a belt that attached around the waist with velcro. When he walks, walk beside him, and you can hold on to the back of the belt. It is amazing how much control you will have. I could easily hold up my 6'2' Dad by his belt. If he did go down I could break the fall and successfully guide him down to a safe landing. That is one reason I insisted he always have on his belted pants when he was out of bed
But no matter what you do, some are just going to fall. More often than not these falls are not major. Dad fell at least a dozen times, only a few even required a trip to the ER, and of those only one had anything other than scratches or bruises. That was a minor brain bleed that cleared itself up in a day. Mom has fallen at least 6 times and has avoided the ER each time.
I finally placed Dad and now Mom under the care of Hospice. At their facility, if they fall, Hospice is called first. A nurse is sent to assess. Only if the nurse deems it necessary does the loved one go to the ER.
Know that this phase will not last. It is just one more transition phase to the next phase
Hang in there!