You can also look into trimming the trees a bit. A good tree trimmer can thin out the crown of the tree, taking out up to 25% of the weight without affecting the shade too much.
Just be sure that they cut the branch without skinning the bark of the trunk. If they cut into the wood of the trunk, the tree will weep and ooze for several weeks and you can invite insect damage. Cutting the branch will not create oozing sap. If you look at the bark you can see where the trunk is and where the branch starts, typically a little bit further out than you might think it does. That bulge of the trunk is what seals over the wound, it has special cells there, so you don't want to cut into that part.
At the start of hurricane season I always give my trees a good looking over to see if any need lightening up. As Rita was bearing down on Houston my tree guy was thinning some of my trees and the neighbors were begging him to work on theirs but it was too late. When those harsh winds blow it is comforting to know that the wind can get through your trees with out breaking branches or uprooting the whole tree.