Yes the first (and best) thing to try is to see if they make shims for your current brifters! That would be a simple solution to the hand-grasping-the brakes issue.
Don't just take an LBS's word for it- see if you can contact Shimano and ask them if shims are available for your model shifters (I assume your brifters are Shimano?).
I thought you already knew that you had non-shimmable brifters....sorry, or I would have recommended this first before changing bars.