Amper,
I worked in the construction field for a good many years and have some knowledge of vinyl siding. Around your windows there is a product known as "J" channel. This butts up against your window and provides you siding a place to go into. This way you do not see the cut ends. Cut your plywood pieces to overlap this area and then run screws in between you window and your "J" channel. You are guaranteed to hit a stud and it won't put holes in your siding. Hope this helps. Good Luck