Solder the JST connector and switch directly to the pads on the QT Py ESP32 Pico. This makes for a very small form factor which is easy to hide in your hand or your pocket, with no distracting wires or lights to give you away.

Flip the QT Py over so you're looking at the back. Trim two of the legs off the momentary switch. Solder the remaining legs to pins G and M0 (aka 13) -- the legs should line up just right with the holes. Make sure the button is placed above the board and not sticking out on the side.

Find the tiny + and - pads on the back of the board behind the USB port. Solder your JST connector + and - pads or legs onto these pads. Be careful - you don't have a lot of room, and if you bridge the pads with solder you'll short out your project. 

I found it helpful to momentarily plug the battery in to the JST port before soldering, to be sure I had everything the right way around. Don't solder + to - or you could fry your board.

Plug your battery into the JST port. I added a zip tie around the battery to keep the wires from pulling out. Test to be sure it's working, then secure the battery to the board with another zip tie, keeping the button accessible. 

You could also add a tiny on/off switch, but I like to keep it small and simple -- simply unplug the battery to turn the device off. It will drain the battery the whole time it's plugged in, since it's constantly "listening" over WiFi. But it will last long enough that you can impress people with your "magical" control of your lights.