Just go to a bearing supplier and buy a pulley with a sleeve to fit the motor shaft, about half the diameter of the lawn blades. Fenner does a whole range of pulleys that are taper lock and which you shrink onto the shaft with a setscrew. Then you keep the motor in the same orientation as it was in the mower ( you probably can use the same chassis for it) and mount the alternator so the pulley matches up the new pulley, then buy a V belt ( same bearing supplier or the car spares place) that will fit. Make the mount for the alternator adjustable to enable you to get the belt on and tension ir as well as get a belt size that fits. Then put the battery there, and you will be good to go. Remember to change the oil and service the motor, it will still need the regular annual service.
If the alternator is one driven by a flat serpentine belt and you cannot get a matching pulley then the simple thing is to buy a 2 or 3 groove pulley for the motor ( same shaft inner mounts it) and machine the inner ridges away to fit a flat belt then use that, or you have to pull the alternator pulley off and get a v pulley for it.
I did that this year to replace a drive pulley that was no longer available that drove a wide belt, as I could not easily change the other side as it is integrated into a gearbox and clutch.
