BT pairing is much improved over previous software versions. I'd try to make the phone not pick up the headphones, turn BT off of the phone.
Go to connections. Go to bluetooth. Tap bluetooth headset. Power on your headphones and hold the button until it goes into pairing mode. The watch will pick it up.
I would add the bluetooth headphone icon to your dropdown menu to quick toggle it.
So if you are on your phone with headphones connected, disconnect your headphones from the phone. Then go to the watch dropdown, tap the headphones icon. The headphones will show up as connected, viewed as a blue dot next to the headphones icon.
From then on, switching between phone and watch will be easy.