NICE Guidelines on induction state as the conclusion to Section 4.10 (pp 61-62):
"In the absence of any other indications, induction of labour should not be carried out simply because a healthcare professional suspects a baby is large for gestational age (macrosomic)."
One of the concerns given includes the inaccuracy of trying to estimate weight prior to birth (8 studies showed the chance of predicting a large - >4kg - baby using sonography estimates to be anywhere between 15% and 79%).
Two randomised control trials indicated no statistical difference in foetal or maternal outcome whether labour with spontaneous or induced. Other (non-RCT) studies have suggested an increase in CS rate if labour is induced.
Assuming there are no other risk factors then I would be asking a LOT of questions about the research behind a recommendation to induce purely on the basis of a large weight estimate given this is contrary to NICE guidance - and quite a few questions on how they can have confidence in their weight estimate to start with! If you don't have confidence in what your registrar is telling you then you should definitely ask for a 2nd opinion.
I'm not sure what I would do if it were me. I do know an extremely experienced MW who's view re. SD was that, if it happens to you, where you are is a lot less relevant than how skilled your HCP's are at resolving it - pretty well everything (apart from a couple of very rare surgical procedures) that can be done to resolve SD can be done in any location, including at home. She had an argument, you were at more risk in a CLU with a MW that was used to pushing a panic button for anything that deviated from normal than you were at home with a MW that was used to having to deal with whatever problems occurred, as speed of action is critical.
That said, all of this came out because we wanted a HB for DD1 and our CMW was very supportive. We wound up with a HB even though we knew she was of above average weight (9lb 12) and breech (we did go out of our way to find very experienced IMs to support us). For me, hospital isn't an environment that I find conducive to birth so I felt HB to be "safer", although trying to do an objective analysis is nigh on impossible. Given that's my starting point, I'd probably start by planning another HB - but that decision is always going to be shaped by previous experience.