A first problem that needs answering is how we're going to integrate the hub motor, i.e., our motor is embedded in the scooter's rear wheel. This is a common design element in electric scooters (no way this can be done with a gas motor) because it saves energy as there's no friction loss from sprockets or chains in the transmission to the wheel.
In our scooter's motor, the axle is fixed and the wheel with the motor inside rotates. Usually, you would expect a fixed motor with a rotating axle. These are in theory the same things, but there's one difference that needs to be addressed; In the scooter, electricity is being fed to the motor with cables that run through the motor's axle, and not via external connectors to the (rotating) motor block.
As our kart's wheels are smaller than the engine, we'll have to build a transmission from our engine to our rear axle. And since I doubt that we will be able to refit the cables to the engine's block instead of its axle, we'll need to find a way to somehow have a (dangerously) rotating engine with a fixed axle built on top of our kart (e.g., by reusing the fork of the scooter's rear wheel, welded to the kart's engine mount). Additionally, we'll have to fit the rotating engine with a sprocket in order to distribute the rotation to our kart's rear axle and wheels.
So, there's a little bit of progress, and a little bit of extra complexity now. There'll be more to come when we get the keys to our scooter.