Will not work.
The Apple Watch is an iPhone accessory, and requires an iPhone to be paired with it.
Do not think about using your own iPhone, as you will then be giving your son full access to everything on your iPhone. Your phone calls, your text messages, your address book, etc...
A cellular Apple Watch shares the iPhone's phone number.
Also the Apple Watch extends its battery life (keep in mind it is a tiny battery), but trying to use the iPhone for radio communications when it is near the radio. Apple does not expect you to spend 24/7 away from your iPhone. The battery depending solely on the cellular radio would have it battery depleted in several hours (much less than a typical day before bedtime).