A friend here in Tucson who likes to do things his way decided to eliminate the air system for all the doors in his Hawk. Here are a few pictures (not great) which I took with my phone on how he did the mains. From what I saw it works well.
He uses a spring attached to keep the doors open once the gear is out. He put a small flange (deflector) on the outside of the gear door to help keep the door open using the air stream.
He did not like the way the flaps were hooked up so he ran the push rod on the bottom outside of the wing and used a horn on the outside bottom of the flap.
You can see part of it in one of the pictures.
He is a inovative guy.

Stan