My situation is different from the OP, but I think there are some relevant lessons. I wont say what they are only to tell my story and let people draw whatever conclusions they want.
I am disabled and use a mobility scooter. It is larger than usual, lot of room in the footwell and with a large basket on the front. I have a much more compact one to use on the train and other close confines. Now I can walk, people think that because I use a mobility scooter I must be like Steven Hawking, and some don't like it when they see me get off it. But I never claimed I couldn't walk, only that I cant walk far and there is a price to pay later for anything I do. More to the point my disability benefit assessors know I can walk, as do my doctors etc it has never been hidden from then or any official record. I still do many of the things I used to do, and I can still exercise, particularly swim. I am disabled for reason x, it matter not to anyone here what that is, only that it is real and it entitles me to the privilege of using mobility equipment.
The mobility scooter is liberating, in many cases it is an out and out advantage. I can trundle down the supermarket or in a mall, take enough items to fill a car boot and go home without having to get off my chair. I then put the scooter away and carry the goods around the house putting things away. It is easier and more convenient than using a car the vast majority of the time. It is worth every penny.
When on the scooter I got far more respect and polite treatment from people I met than I ever received while walking. It was surprising at first. I get to see the nice side of people a lot of the time. There is more support out there than many people think and it is rather warming frankly.
I see many people who ask about my scooter. 'Oh I always wanted one of those.' 'Yes, they are worth every penny. Highly recommended, it will make a lot of difference.'
A lot of thought goes into making the lives of disabled people more fruitful and pleasant. Tap into that without shame and spread the hope.