As long as the controller itself has a "normal" throttle input, then first verify the connector wiring:
Use your voltmeter on 200VDC, with the black lead on battery negative of the controller. Turn on the scooter. Red lead on red throttle connector wire should get about 5v, if that's power to the throttle.
Red lead on green wire should get about 0v; hold wheel offground and slowly turn throttle--if it suddenly jumps to a steady voltage and doesnt' change more, it's an on/off throttle. If it slowly changes form about 0v to about 5v, (or from about 1v to about 4v), it's a normal throttle that can vary the speed.
Red lead on yellow wire (each one) should get about 0v, if they're ground.
If so, you can install the pot on that green wire, regardless of what kind of actual throttle is used:
Cut the green wire halfway between controller and connector.
Center wire of a 5kohm to 10kohm pot goes to the green wire on the controller side.
"top" wire of the pot goes to green wire on connector side.
"bottom" wire of the pot goes to ground; this gets spliced in like a "T" to the black wire.
Adjust the pot to the center, and it should now have about half the max throttle ability. Adjust up or down from there to suit your needs.
This does not just limit the max speed, but also the max acceleration.
If the wiring didn't measure out as noted above, then post what readings you did get so we can figure out where to put the pot.
BTW, another option is to replace the on/off throttle with a regular throttle (potentiometer type, not hall type), rather than adding the pot, and then she'd be able to control the speed herself. Or you can actually add a "limit screw" or pin to prevent the throttle from being physically moved beyond a certain point, but if she's the cautious type as you say, she'd probably do fine with controlling it herself.
If the controller itself is just an on/off type, then you may have to open it up to install the pot to limit it, and do some investigation of the circuitry inside. (which we can help you with). Some of those are potted solid, and may require dissolving the potting. It's probably easier to buy a new (brushed) controller that does have a normal throttle input, than to do this.
Also, some of these don't use actual controllers at all. They use a board with relays (like this one:
https://endless-sphere.com/forums/viewtopic.php?f=35&t=89541
but if you have a metal heatsink-looking box then yours probably does use an actual controller, which probably does have an actual variable throttle input.
