He uses flat wound, even on the Ricky.
I bought a 1964 re-issue from a Hofner dealer at the Liverpool convention in '97, he's the guy who has the bass that was stolen from Paul in the 60's and tried to sell it to Paul.
He said Paul uses flat wound, the bass came with Clib 62 Josima strings (Hofner strings made in Germany). I bought an extra set at the time, no, they are not for sale. The address of the dealer Music Ground is 51 Hallgate, Doncaster, S. Yorks Engand DN1 3PB
I decided on the re-issue rather than an original for the main reason is the re-issue is actually playable and stays in tune because it comes already modified with the rod in the neck and the neck bridge is fastened to the base much better, other than that it looks and sounds great.
I made the mistake and put round wound srings on my '76 Ricky and it just don't cut it. Haven't used it enough to put flats on it yet.