There is absolutley no need for an induction before 42wks if there are no other medical indications, eg low fluid levels, baby in distress, PE in you.
There is a greater risk of interventions and CS with inducing a baby which is not yet ready to be delivered and just being past 40wks is not a valid medical reason to get baby out.
Term is regarded at bewteen 37 and 42wks with 40 being the average. You're not actually overdue till 42+weeks and even then you may just be a slow cooker.
You can ask for expectant management instead.
Induction is my bug bear so please bear with me, I'd like to try and give you as much information so that if you CHOOSE an induction it is for reasons that you are happy with not just because the HCPs say you should have one. They are only offering you one, you are allowed to decline it.
Radical Midwives and induction
Kent Midwifery Practice and induction
If you have a sweep, be sure to ask what your Bishop's Score is, if it's lower than 8 or 9 then an induction is highly likely to be traumatic! Can't find the link I would normally post with this info so bear with me, I'll get back to you.
I hope that you can make informed decisions, so please ask for all the pros and cons for any procedure they 'offer'.
Also I'm not sure if I've made enough sense as I have a little lady nagging at me, she's not 100% at the moment....
Sending you happy, calm labour vibes!