I just wanted to pop in with my experience. Although I didn't have any growth scans, my midwife always said I'd have a "good size baby". Thankfully she never estimated the kilos because I went on to have a 4.1kg baby boy. If she had've told me that's what she was expecting I would've spent the later weeks of my pregnancy freaking out! But I now know that the weight of a baby does not determine the outcome of your labour/birth.
Like you I didn't have G.D & probably didn't really trust my body (if I'm going to be honest). I birthed my son with no drugs, intervention or stitches. You will amaze yourself, trust me. As others have said, a 4kg baby isn't too big for you to birth. Don't let yourself be talked into something you're not comfortable with. You CAN do it!
Hope that helps - all the best for your upcoming birth!