Can i use a 450W ebike controller instead of a 500W?

I dont see why not unless controller has a minimum wattage requirement? Someone that knows more will chime in soon im sure..
From what i know, controllers are rated by Amperage, not wattage?
Amperage i believe is load? And some point the two will be the same. Lets say for example 500 watts may be around 15 amps. I know my 35 amp controller sees about 1450 watts max. But batteries i believe effects that rating as well. As of course tire width,size and drag may effect top speed as one would think Amperage at a given speed with a narrower tire only may have an effect on Amperage output? anyone with a lot of experience in this field care to offer an opinion? Perhaps im wrong on some accounts? Or maybe all? Haha! Nothing wrong with asking questions!