Delivery

When I had my son 5 years ago he was only 6lbs 14 ounces at 41weeks. pregnancy was perfect but delivery was a nightmare. I was induced and baby got stuck had to have vacuum help get him out. I got really sick and spent a week in the hospital. Pregnant with my second and have gestational diabetes this time. At 36 week ultrasound dr said that baby was at 6lbs 4 ounces. At my appointment today at 37 weeks said that she thinks I'm ok to do a natural delivery and not a c section. But at 36 weeks baby is just 10 ounces smaller than my first son and they aren't doing anymore growth scans. My family is mad says I should say I want a c section and that it's too dangerous to try natural. That baby could get stuck and lose oxygen if they can't get him out. My first delivery was a nightmare and she did say a baby bigger wouldn't fit so is it safe to try a natural delivery with this one? Ive been afraid of delivery becauae of how scary the first one was and to constantly hear my family say how dangerous it is just makes it worse. I just want my baby here safely. Anyone have a experience like this where they would be delievering a baby bigger than what they were told they could deliver?