Just watched a video review of the library, it sounds really nice!
After skimming the manual, it looks like CC11 (Expression, the default CC for breath on the Sylphyo) is taken into account with the Armenian Duduk, the Turkish Ney, the Persian Ney, and the Zourna. CC2 seems to be used as a switch (to turn on/off the speed knob) rather than as a breath controller. CC1 (the default CC for the slider) seems to control how velocity influences the way legatos are performed.
So based on the manual only (couldn't find a demo), I'd say you could use CC11 with a fixed velocity (100 rather than 127), or maybe with dynamic velocity, as velocity seems to influence legato. But don't take my word for it: we don't have the library here, so the best thing to do would be to ask the library developers themselves!