If I want to play fortnite, could one player use keyboard and mouse while the other uses...

I've learnt that sometimes it's easier just to try it and see what happens, I think this is one of those times, there may be some trouble shooting that needs to be done.

Yes, it’s possible. I have seen people do it before. Unless it was patched within the past two months. Won’t hurt to try it out for yourself, though.

I have not attempted this unfortunately but the best option would be to give it a try and see if it works. Please let me know the outcome!

For the following to work you must make the menu selections using your keyboard. If you use the controller to make your menu selections to start the game you will be placed in a room for those with a controller and your keyboard/mouse will be non functional
to make it fair to other players. To enter the room for keyboard and mouse users the game must be started by selecting the options using the keyboard/mouse. Hope this helps.

Mouse and keyboard support

Fortnite on Xbox One supports the ability to play with a mouse and keyboard. Note that when using a mouse and keyboard on Xbox One, you’ll be placed in a game with other users who also chose mouse and keyboard as their control option. To enable your setup
to use mouse and keyboard, see Mouse and Keyboard Support

Note If you’re on a child account, you’ll also need to enable settings for cross-network play to use a keyboard and mouse while playing
on Xbox One.

Currently only Minecraft (without the "Xbox One Edition" in the title) is playable with keyboard and mouse.

All other games, including Fortnite do NOT work with Keyboard and Mouse on the Xbox One.

If you want to play Fortnite with Keyboard and Mouse, you can do that on a regular Windows PC.