The lifespan of a virus "in the open air" outside the human body is relatively short.
Between 1 hour and several days depending on the virus.
It also depends on the contact surface, the external environment... (temperatures, humidity levels...)
Let's imagine an infected Chinese watchmaker that assembles your watch and coughs on it.
She's then stored, packed, shipped, passes in trucks, waits at the sorting center, gets on the plane in a hold between 5 and 10°, changes climate, arrives in your country, waits at the sorting center, gets on trucks, arrives in your mailbox. And all this between 10 and 20 days depending on the country...
Frankly, the chance of catching the virus is almost nil, especially if you don't lick the watch it comes from.
If you really want to be careful, put gloves and mask on when opening the package, throw it away quickly and disinfect the watch.
But it's more for your peace of mind.