There is no need (nor any way) to turn off the watch whilst it is charging.
When you have Wrist Detection turned on, you will only receive notifications on Apple Watch if your iPhone is locked or asleep and your watch is on your wrist and unlocked. Otherwise, notifications will go to your iPhone.
On your iPhone, In the Apple Watch app go to: My Watch > General > Wrist Detection - turn this on.
Also check your Do Not Disturb settings on your iPhone (Settings > Do Not Disturb).
If notifications are not behaving this way (and Wrist Detection is turned on and Do Not Disturb settings are correct on both devices), try restarting both devices:
- Restart Apple Watch: Press and hold the side button until you see the Power Off slider; Drag the slider to turn off completely; Afterwards, press and hold the side button until you see the Apple logo.
- Restart iPhone: Press and hold the Sleep/Wake button until the red slider appears; Drag the slider to turn your iPhone off; When it has finished turning off, press and hold the Sleep/Wake button again until you see the Apple logo.