Send controller inputs to two devices

As mentioned in the comments, a short press of the Sync button instantly turns off a Joycon or Pro controller. There are no other shortcuts for this.

Games which behave nicely will update the number of controllers that they support, automatically turning unused ones off for you anyway.

The only things from your process that I see might be an issue are that:

• only the black USB-A cable needs to be connected from the adapter to the Switch dock
• and you have to hit both the L and R triggers on the Gamecube controller to link to to the Switch after you connect the adapter with the controllers attached.