If you are worried about cord prolapse then just opt for a pessary

They will only break your watersif you score a certain number of points on the Bishops Score...usually that involves being around 3cm dilated, your cervix being quite short and soft...if not then they will not break them. I cant remember what score you have to get on the Bishops Score, sorry.
With my second baby, he was floating free when I was induced at 40+3 (induced due to repeated reduced fetal movements). I was given a Propess pessary which they inserted at 7pm on a wednesday evening. With Propess they leave it in for 24hours and then reassess you after your 24hrs is up (if you havent had baby by then).
6am the next morning (thursday) I started having contractions...they were coming every few minutes and lasting 30-40 seconds. They continued to get stronger until about 4pm that day when I was begging the midwife to check me for progression becausse I was in agony. They put me on the trace...contractions were registering up to 70 on the chart and coming every 1-2 minutes. The amount of pain was horrid. Finaly, they agreed to an internal but was on,y 2cm.
Basically, all of these strong painful contractions were not doing much to progress me but were working to move the baby into position. I was checked again at 7pm (24hrs after pessary was inserted) and I was just about 3cm so I was able to go to labour ward and have waters broken (no room on labour ward until 4am the next morning though arrggh). Pessary was removed at 7pm. Contractions stopped completely.
Went to labour ward for waters broke...they left me for a few hours to see if labour would start but it never so I was put onto a drip at about 8am. Was on the syntocinon drip all day up until 2pm when it was cranked up to maximum and it still wasnt bringing on my labour and I was still 3cm! No pain no nothing! All of a sudden I just started contracting at about 2.30pm and he was born at 4.39pm on the friday (nearly 48hours after induction started).
Sorry for the long post, just trying to give you as much detail as poss about timescales

Moral of the story for me was that because he was so high up it took a lot of work for my body to get him into position and it took a lot of painful contractions to get him there! But once he was there and I finally went into labour it was much more straightforward. There was no real risk of cord prolapse because by the time my waters were broken I was already 3cm and babys head had come down into position.
Hope that helps xxx