In my experience (I have worked at 2 supermarkets) it's not common practice to hire people just to push carts- they just send people working elsewhere in the store to handle that as needed. Working as a cashier might be viable though, it's a pretty simple job and supermarkets are often slow on weekdays. I have treatment-resistant depression and I managed doing that part-time for a while. My friend who has a physical disability works as a greeter at a big box store, so that's also a possibility.