I have a character, Droven, who loses an arm in an accident and becomes an amputee at the shoulder. Due to the circumstances of the setting (zombie apocalypse), he is unable to get a prosthetic and must go through the rest of the story with one arm. I want to make it clear that this character does not become weaker or less useful because of his loss, but find other ways to make it through this world. I myself am not an amputee, nor do I know any that I can speak to easily. I have done personal research, but if anyone on here has any advice on how to respectfully write this character so that he is not a stereotype, I would appreciate it.
Honestly, you could show how they've adjusted to their new normal, without making them an outcast. I have a few in my world setting and I treat them like the average person; my character Kamari deals with the loss of his eye and arm by maintaining the health of the rest of his body and working at the same pace as everyone else. You can show how it changes them, how their life has changed and how they overcome their injuries.
Of course, not every character with an amputated limb is going to be able to overcome their trauma in the same way, but that doesn't mean you have to avoid it or pretend its not as serious at it is. For some characters it can completely devastate them and can be part of massive character arch to go through the healing process.
Don't be afraid to try some things out and run it by some peers.
Have him use his teeth to help grab things, if it makes sense in that particular context. Have him pin things between his cheek and his shoulder. Possibly have him forget, grumble, and have to compensate at the last moment; but I'd suggest only having that be once or twice. I don't know how much having him use his feet would be feasible under the circumstances; but if there's a time where it makes sense, you do you.
And while the "disabled snarker" trope does have basis in reality? Try not to overdo it.