To play Fortnite on a computer, a mouse is not necessary. Choose your favourite Xbox One or PlayStation 4 controller and go from there. The controllers can be used by connecting a USB connection to a computer. You can use Bluetooth to link your wireless Xbox One or PlayStation 4 controller as an alternative to plugging in a cable.
Settings > Devices > Turn on Bluetooth > Add Bluetooth or another device is where you'll find the option to do this. Keep in mind that the matchmaking process is input-based, so you'll only be paired with other players who are also using a controller.