Could an astronaut use a wrist watch to measure relativistic time dilation?
No, because the accumulated time dilation from the motion of the astronauts and their motion through the earth’s gravitational field amounts to less than a micro-second, and you have to have a measurement precision that is about 100 times better than that over the 1 week period so that you see even this effect. Most wrist watches are only good to a second or so.
