Hide drop down arrows in optimized file

I have a Acrobat form which my general clinics use.  For standardized results there are several dropdown menus.  Once the clinic submits the form to me I will Save as Other>Optimized PDF prior to sending it on to a specialty clinic.  This is so the specialty clinics cannot make changes to the form.  When I optimize/flatten the form the drop down menu arrows still appear.  They don't need to be there when the drop down function is no longer functional.  Is there a way to prevent them from printing to file?