Regarding the avatar, the player should be able to choose. Just like any player, some would like to have avatars that resemble themselves, some would not. Not all visually impaired or blind players would have a guide dog or a cane. It varies a lot from person to person but my advice to be inclusive is just to let them choose, give them options. A lot of people like dogs, so even sighted players could choose to have a dog.

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A controller is just a type of input device. Blind people or visually impaired people should have no problem using it. The real question is what feedback the player has. For instance, would the game be talking? Would it have text to speech? It's not useful to say the player can use the controller if they cannot tell what actions they are doing or what they need to do in the game. An easy way to intuition this is to think if you would be able to play with your eyes closed (for blind accessibility). If you design for visual impariment, there are multiple things to consider, but you will often want good contrasts, customizable font and font size, etc.