There were several stunt and fight choreographers in Casino Royal. Apparently Gary Powell and Bob Anderson, among others worked the film. From what I can tell, they used a mish-mash of various RBSD systems, drawing heavily Krav with a bit of BJJ thrown in for appeal, but blended to look good rather than be most appropriate. Stage Fighting is not the same as real fighting. The primary goals of the two are, in fact, diametrically opposed. In Stage Combat, the goal is to keep everyone safe while telling a story; it has to look good and subtlety is bad because it makes it hard for the audience to follow. It real combat, the goal is to kill the other guy and break stuff off of him; it doesn't have to look good it just has to work and subtlety is very useful because it makes it hard for the opponent to follow.
Now, to dip our toe into real life, the original Bond books were based on Flemming's experiences in forming and administering special operations forces for infiltration, intelligence gathering, behind-the-lines sabotage and operations, and counter-intelligence during WWII. The hand-to-hand training for these forces at the time would have been in line with that of Applegate, Fairbairn, Sykes, et all and would be nearest to the modern lineage from those gentlemen, not to tread too heavily on the whole Defendu vs. Defendo spat. The system(s) themselves were typically a mix of period Judo, Western Wrestling, "Dirty Boxing," and a smattering of basic savatte-like kicking. The knife elements of the systems were usually based from a western Fencing background but sometimes seem to dip into the well of regional European knife systems (Spanish or Italian seem good bets to me). Fairbairn's stick system is a hard nut to crack because it doesn't look much like any Chinese stick system. I'm betting he just took a simple "high percentage" method of holding a billie-club/short stick and then applied a dozen "high percentage" techniques to it then declared it "done."
Peace favor your sword,
Kirk