We had very similar, though in our case the fold/fluid was 13.9mm deep at greatest measurement (cystic hygroma).
We were told the same as you. However, we opted for the amniocentesis after research - the consultant who did ours is pretty well known in the field of fetal medicine and said that in however many years of doing amnios (pretty much since they'd been introduced!) not one viable pregnancy had miscarried; all those who had miscarried within a couple of weeks were, like us, at extremely high risk of miscarrying anyway and all the foetuses had conditions incompatible with life, as the amnio proved.
The reason we did the amnio was because whilst we wouldn't have terminated under many circumstances, partly because of recurrent miscarriages, I am not sure I could have carried a pregnancy almost or to term knowing that there was no way the baby could survive birth, especially as we had DC1 to think of - and because if we didn't terminate and the baby was likely to be born with abnormalities such as heart problems, we wanted to make sure we had the best possible team on standby for the birth, fully prepared and ready to operate immediately to give best chances if necessary. We did have a lot of scans as well - have you been offered detailed cardiac scans, etc? We were sent to various specialist hospitals, Kings, Evelina at Tommy's, etc for different specialist scans.
The fluid reabsorbed eventually. DC2 was born at 38w by ELCS, just under 9lbs, looking like a little rugby player. He had a thick neck (but we were looking for it - he also had rugby thighs!). No abnormalities. He's now the skinniest 4yo imaginable despite still having the appetite of a rugby player.
Wishing you all the best, it's a horrible time and made worse because it should be the happiest time - but it is difficult to be happy and make plans when you're so fearful of unknowns.