How do I stop flashing lights and change Apple Watch band?

The green light on the back is a blood flow sensor, and intermittent showing of the green light is normal.

It should stop of its own accord, either when it times out, or when you are again wearing your Watch.

If the green light (or the red light) doesn’t shut itself off as it shortly should, yes, you can restart the Watch.

Monitor your heart rate with Apple Watch - Apple Support

Try shutting down the watch. To shut down your watch, press and hold the side button until the sliders appear, then tap the power icon in the upper right corner. When the Power Off slider appears, drag it to the right.

To start up the watch after changing the watchband, press & hold the side button.

M1 Mac mini, macOS 15.3.1;  Watch, series 10 GPS-only, watchOS 11.3.1; iPhone 16, iOS 18.3.1; TV 4th Gen, tvOS 18.3; HomePods, audioOS 18.3 and Airport Express w/ Airplay 2

Did you try to switch off the watch, before changing the wrist band?

Change your Apple Watch band - Apple Support

The green light is the wrist detection sensor.