Unfavorable Cervix/Cervical Ripening

I'm at 40+2 & my doctor says I have an unfavorable cervix. I'm not dilated or even close to being & I'm barely having contractions. My last exam was on Wednesday. The doctor doesn't really want me to go over 41 weeks. This has been a healthy pregnancy, baby moves just fine & his heart rate is normal.
My doctor has offered the option to go in tomorrow night to have a cervical ripening done with the use of Cervidil. I was told that it can put anyone at a higher risk of c-section & that it may or may not even work.
If he doesn't arrive by Monday, then that day I will go in for a sonogram, nonstress test & will be scheduled to be induced next week some time, possibly even that day. 
Has anyone experienced this? Should I do the cervical ripening knowing it could fail & I may end up being induced anyway? 
Thanks in advance!
**Update- I called to cancel the ripening in hopes to just go on my own & see what Monday would bring me. The nurse called back wondering why & I explained. She said tomorrow night I should plan on staying & they'll use cytotec to jumpstart labor & if no baby by Sunday morning, then they'll start the actual inducing & hopefully "if all goes well" I should have a baby Sunday. I asked what the appointment on Monday was for if they were just going to induce me Saturday & that was a just in case there's no baby yet. Sooo hopefully this is the right thing. The nurse reassured me that this is super common with an unfavorable cervix & most women end up having their baby the next day.