You can pick and choose your size of motor, then decide how long you would like to run for and pick your battery pack. The larger the charger you pick, the faster it will charge, assuming it doesn’t require three phase or 240V charging which you might not find at your local kart track. Either way you will waiting in comparison to adding gas.
One thing to keep in mind when designing an electric kart power train is that the torque is instantaneous, it doesn’t build up like a 2 stroke or even 4 stroke. So in my opinion you can get away with a lower powered motor and still get the same feeling or rush and you will find you will run a much smaller gearing to make use of that torque from zero rpm.