Shedding doesn’t necessarily mean that the hair was killed for good. It takes a certain amount of heat to disable the follicle permanently. So yes, it’s best to treat at highest setting your skin can handle without burning, not matter what laser they use.
If they switch to a Yag, they would need to be aggressive with settings on it as well. I don’t know if they’re treating you at a low settings because they’re conservative on settings on general, or because they don’t know any better.
You can ask them to test spot higher settings on LightSheer to see how high you can go. If you can’t handle 25J, Yag would be better. But then the settings on the Yag need to be good too. So it’d be best if they tested for how high they can go on that as well.