I can't think of any bike with a 4mph throttle that can't be changed by a simple user-setting to a full-range one.
The motor controller is the biggest obstacle to fitting a throttle. Most of the older ones have the connector, even if there's no throttle fitted, but more recent ones don't have the connector.
You can fit a throttle to any of those typical Chinese bikes. It's only a case of how much work you have to do. If you have a 4mph throttle, it's a simple setting. If you have no throttle, but the controller has the connector, it's plug and play. If you don't have the connector, you have to change the controller, in which case total cost would be about £25 for the cheapest rubbish one, £40 for a reasonable one and £70 for a really nice one that will be a big improvement to the bike.
All throttles work the same electrically with three wires for the throttle function. Some have additional features, like built in LCD, power or light switch, battery indicator LEDs, etc. You will see them with different lengths of wire and different connectors.
Another important factor is how they fit on the handlebars. Sometimes, shifters or brake levers get in the way. The easiest to use and most likely to install successfully are the plain basic thumb throttles. Don't get a full width throttle, like you have on a motorbike. they break too easy and are not very easy to modulate on a bicycle.