I believe my neighbors now knows me as “that weirdo who walks their cat”

Solidarity my brother/sister.

At first he just went mostly where he wanted to go. But I've been working with him several years and he's got a few commands down. If I tug his leash and say "this way" or "come on" he'll turn and follow me, "psh psh" means 'hurry up', and "be good" means 'stop trying to get in trouble and sit down'. He knows the route we usually take around the neighborhood and is good about following it.

My other harness kitty has been wearing harnesses pretty much since she could walk. You can walk her like a dog. You really don't even need the leash most of the time, she knows "harness = going for a walk, stay close."