I'll take a crack at it, I'm sure there will be a flood to follow....

Before I begin, I must say that you have an interesting hanger full of airplanes for a "corporate" flight department. I know we are all interested in the operational details if you can share. With the aircraft you'll be operating it's going to be difficult to find someone with extensive operational experience in rotor wing, heavy international, and bizjet ops. However, there are some excellent aviators with equally impressive managerial skills out there.

Because this individual may not fly in the operation everyday, I'd put leadership credential over flying experience, although both are important. My short list of things to look for would be:

Organizational leadership with real industry experience
Integrity beyond reproach
Productive industry contacts
Loyalty to pilots and owners
High intellect that allows him to understand complex problems (and solve them)
An excellent aviator

I'm sure I'll think other qualifications after I send this.

Good luck on the search, how does one contact you?