If you need it normally, I’d take the stick. Interviews are nerve-wracking enough, so you should be trying to make yourself as comfortable and confident as possible. It’s a bit like NOT wearing a brand new suit on the day - it should be something smart, but which you’ve worn before, so it doesn’t feel all new and strange.
I’d say the added worry of doing without something you normally need, and possibly falling over in front of everyone is something you can well do without.
Better to turn up with a stick than fall over on the way, or actually in the building. I think it’s very unlikely they will ask about it, as it’s rude, as well as probably illegal.
In the unlikely event it does crop up, I’d resist any temptation to fib (e.g. the “old sports injury” story), as that could certainly backfire if you get the job, and it becomes obvious you lied. But you could acknowledge an unspecified “neurological problem” - which is true, but sounds less scary than “MS”.