It's a while back since I had the cellular plan active on my Apple Watch, but I was able to send iMessages with it while away from my iPhone.
Maybe a silly question, but the contact you messaged (that was green) are you normally able to send them iMessages or have they recently moved to a none Apple device?
And also, has the contact in question decided to switch off their iMessage setting?
Maybe worth a try on your iPhone, go into Settings, and then turn the iMessage switch off, turn your iPhone off and back on and then turn the iMessage switch back on. Your Apple Watch should mirror these settings, so it should be able to detect that you have done this. After that, switch off you iPhone and make sure your Apple Watch is NOT connected to WIFI (switch WIFI off in the Apple Watch's Control Centre). Your Apple Watch should then be connected to cellular, and see if you are then able to send an iMessage.
If that doesn't work, try signing out and back into your Apple ID on your iPhone. To do this go into Settings, and then touch the very top part where your name is shown. At the very bottom of the next screen you should see sign out. Switch your iPhone off and then back on, and sign back in and see if this sorts the issue out.
