I think one aesthetic challenge, when trying to follow the original style, is packaging the battery. The motor is no problem: an exposed motor running a chain drive would work fine, and look right. Even a modern electronic controller is no problem, because it is small and can be tucked under a seat; it could also be housed in finned cast aluminum box which would look right at home. A charger could be housed like the controller, or just left at home or carried in luggage".
The battery is big, and doesn't look mechanical. I suppose the answers could include:
- use a modern lithium battery of moderate size and enclose it in what looks like a fuel tank (although a cyclecar would not have a large fuel tank), or
- use a modern lithium battery of moderate size and hide it under the seat, or
- use lead-acid batteries (accepting the resulting short range), mount them in the open, and insulate all connections for safety, or
- use LiFePO4 prismatic cells, install them like the lead-acids, and manually check their individual states of charge after use and after charging.
One of the old control schemes could look interesting, but it needs to be kept safe (safer than those old electric cars were).... and seriously, I wouldn't want to build one, especially the kind with resistors.
With a 48-volt (nominal) battery in four sections (such as four 12-volt lead-acid batteries or four 4-cell lithium modules), you could use a "golf cart" motor, and arrange relays to implement the voltage-switching scheme shown on Lee Hart's controller page (from the Henney Kilowatt) or a variant with more contacts and no diodes, if you can stand only crude steps in power (12V, 24V, and 48V). The pile of cables and relays would look vintage and suitably primitive. It would be more expensive than a ready-to-use electronic controller.