Reddit mentions of Kingsley Mini Nylon Nail Brush-White

Awesome, thanks! Is this what you mean by a nylon nail brush?

Nickel is harder than brass, so unless the plating is already damaged a brass bristle brush won't hurt it. I have used one on dozens of vintage razors so far and it hasn't hurt the plating yet. Just don't use it on a gold-tone razor as it will scratch the gold off.

To be clear, I am talking about a brush like this, not a grill cleaning brush or something.

If you are really worried, you could get a nylon nail brush, which will also work but won't work as well.