Patty .....
From the sounds of things your hair is already very short, which is the way you like it and are more comfortable. Since your surgery is scheduled for next month, you will have warm weather months (unless you leave in the Southern Hemisphere) afterwards. I would vote on just keeping your hair like you usually do.
As others have said, most surgeons lift back your hair and only shave the 2" strip or so that they need to have clear. By the time I returned home from my out-of-state surgery, my friends said "I thought you had surgery on your head." So, I had to lift up my hair for them to see it.
Because of your short hair (and as is the case with most men), your incision area will be more noticeable until your hair grows back, which usually happens very quickly. If you are like many of us, you will probably be among family and friends for most of that "growing back in" time anyway.
Keep us posted. Clarice