Replacing Ceiling Fan That Has Separate Light Fixture

I have a Hampton Bay fan on my porch, as well as a separate light fixture. They are both controlled by a Hampton Bay remote, and are both wired to the same wall switch.

My light works well, but the fan's rotation is way too slow and a new capacitor didn't fix it. The fan is old and not the style I want, so I'm prepared to replace it.

Is there anything I need to consider about replacing the fan, knowing that I still want the light to be controlled via remote? I'm worried that if I replace the current fan with a new one, I won't be able to control the light anymore.