David, I also own a 'blued' (really more black to me...) P99, but I believe the polymer and coating (Tenifer) are the same between the green and black, just different pigments, therefore should clean up the same. However, YMMV, so proceed at your own discretion.
I just spoke with Earl today regarding how to clean the frame, trigger group and striker assembly, and his recommendation was to spray liberally with KleenBore Formula 3, which apparently is both a degreaser and lubricant at the same time.
The rest of the gun can be cleaned with standard techniques - Hoppes #9 for the barrel, slide scrubbed with Hoppes and a toothbrush, then relubed with CLP. Exterior should be wiped down with a silicone rag, and that should do it.
Enjoy your P99!!!
HTH