Assciation bylaws can not stop you from protecting your property. The courts have ruled time and again in favor of the resident when it comes to shutter deployment. The recent 'no-name' storm that hit the Florida gulf without warning is a perfect argument. If your association has fines for deployment - then they assume the risk of loss. Your shutters should provide egress in the event of a fire - for local fire codes.

What do your documents say? Is their anything in them that prohibits this?

You are under the rules of the HOA.