Feel free to roll up your cuffs, relaxed and casual, leaving no trace, put on your watch, natural and graceful, low-key and meaningful. It means nothing to the general public.
Go outside. If the cuffs are bigger, you can take them in. Otherwise, put it in your pocket or not.
Of course, it is worn outside the shirt, especially on formal occasions. A watch is a symbol of one's taste and status. Watches can reflect temperament, so it's unsightly to unbutton shirt cuffs and look at watches.