I agree with you, at this point I would not fiddle. There is no medical indication on why you should try stripping your membranes. My third child came 13 days past my due date and we were considering it if I did not go into labor spontaneously. At this point there does not seem like any reason for you to try to move it along.
Stripping the membranes can introduce germs to the area. If you are strep positive you should be more leery of this (and all vaginal exams).
If there is medical indications, high blood pressure, eclampsia, no/low amniotic fluid, et then it should be "considered" for first attempt to get labor going.
Another risk is possible breaking the waters.
Again weighing individual risk and medical issues is important.
I know in my situation with my third child the risk of stripping membranes could have been worth it to avoid pit and/or other more intrusive induction procedures. It was the least invassive. Also, if I would of had it done it would of been at the doctors office and I would go home after.