you can ask. whether it will work depends on the cervix, if it's too far back they might not be able to do it.
I'm probably dumb, but I never heard of needing to be induced because baby is small. surely that would be the reason to wait longer, no?
it's a genuine question, I wonder why you can't wait to go to term and beyond, sweeps are not normally offered (or asked for) before 40 weeks and even then not all of them work.
the only thing I will suggest is to have sex. (not advised once waters are broken for ris of infection)
the sperm contains something (can't remember the name) that can help ripen the cervix.
if yuo can have a seep I would strongly advise you to try and have sex as quickly as you can afterwards - it's been the winning combo for us 3 times - with DS3, DS5 an DD!
That is actually a 100% success rate for us, as the other times the sweep couldn't be done etc.
(DS1 - waters broke, so no sweep offered and had to be induced as labour didn't progress
DS2- they couldn't reach the cervix, so sweep couldn't be done and had to be induced.
DS4 - was ELSC as he was footling breech)
I hope you have good news on Monday, but if I were you I would strongly question the need to be induced, if there's no other reason apart from baby being small (which of course can be a very valid one, it's just it seems strange to me, sorry)