It depends on you. I would schedule a scan to make sure baby is fine, especially when you’re already at your EDD. If you call up the hospital, they will advise you to go in when you feel contractions/lose your mucus plug or water bag break. But if you insist to go down, they will just charge you for the CTG scan, checking of dilation and etc if you are not giving birth. But at least you’ll have a peace of mind. (I did this)
You can time your contractions, as soon as it gets too intense and too frequent (and last longer), can call the hospital then prepare to go down.