Thanks all for your input and work towards this!
I would agree with the tooltip on the clients list page, but would suggest to make it visible without the need to hover (like in @johnny's first implementation) in the client details page. This allows for hassle free retreival of the client ID if already on that page and if for example you're on the phone to that customer.
I would also like to suggest placing it somewhere on the invoice & statement. Many clients who pay recurring invoices would simply use their account number (as automatic payments would be static and the invoice number changes).
Great work in any case though guys, much appreciated.