Hi OP, I refused induction and baby came at 41+6 in the end - I went into labour naturally, but I did end up having the drip late on in labour as my progress stalled. I'm very glad I waited though and didn't have the earlier induction as I am sure it would have ended in a c-section if I had - my labour was long and my body basically just needed a bit more time to do everything. Baby was perfectly healthy. Here is a good article on this by Dr Sara Wickham: www.sarawickham.com/articles-2/induction-of-labour/
Induction for post dates alone (e.g. being 'overdue) can cause a cascade of other inteventions, stress for you and baby, if your body isn't ready, because every baby and mother is different, and some babies do take longer to 'cook'. I would say to follow your instincts on this - if your instinct is to wait a few more days, then do that - you could go in for a scan in a couple of days instead to check on baby's well-being. You can also opt for increased monitoring from 42 weeks if you wanted to rather than having an induction. Most babies do come before 42 weeks and it is extremely rare for a baby to come after 43 weeks so you have at most about a week and baby would very likely be here, with or without induction! Induction is also not without risks - so it's about weighing those up with your current situation (the risks of doing nothing for now) and then doing what you feel is right. Your midwife has no idea whether breaking your waters will be enough and shouldn't be advising you it'll be this 'simple' necessarily. She should be properly informing you of your options and the risks and benefits, not effectively trying to convince you to have an induction.
Induction before your body/baby is ready is more likely to lead to an instrumental birth/c-section. Of course inductions can also go smoothly, and you may find it just helps speed things along... but scientifically, the 40 week due date is artificial, in reality it is a due 'period' from 37-42 weeks and baby isn't overdue until 42 weeks is up. To make a decision use the BRAIN acronym - Benefits, Risks, Alternatives, Instinct, Nothing. I.e. weigh up risks and benefits, consider the alternatives, tune into your gut instinct, and then consider what would happen if you did nothing e.g. what if you waited one more day?
I'm sure you'll make the right decision. Just remember it's your choice, and you are entitled to ask questions and explore alternatives x