GPS receivers are receivers, not transmitters. Therefore they cannot interfere with any other device.
"Flight mode", on devices equipped with it, are designed to switch off transmitters. But your watch has none in the first place! The only reason i can think of to switch off GPS would be to conserve power.
Most countries have lists of electronic devices that are permitted to operate at all times in flight. The lists include personal watches (and pacemakers, etc.)
So I would not worry about it. Use your watch anytime you like.