Rolex Tudor Oyster Identification

[Oysterlady]

I'm a new member and hope someone may be able to assit me.
A friend gave me this watch as he is almost blind and it is no longer of use to him. I'd like to identify it's date of manufacture and if possible it's value. It seems to work ok. The winder seems to be on a spring which pushes in, for what reason I'm not sure. The back of the case says "Original Oyster Case by Rolex Geneva". I can't see any serial numbers anywhere and sadly no longer has it's original band on it.
I live on the South Coast of New South Wales, Australia and would appreciate anyone who could advise me on who to talk to as reading the posts here I understand the watch needs to be opened by a Rolex expert rather than a local jeweler? Many Thanks, Oysterlady.