Second babies are often a little easier to encourage into the world, it may well be that breaking your waters is enough and you'll labour on your own,
So try not to think about the drip, and agree with others, if you can negotiate a but more time and or cord free monitoring, if they don't do that you could ask for intermittent Doppler monitoring or agree to do 20 mins per hour or something similar. Good luck. Look forward to your BA