Try to take some yoghurt and drink at least 2l of water everyday. You can also try to eat some dragonfruits and dried prunes. Helps for me! But I still get piles and sometimes slight anus tears even though I didn't have constipation during my whole pregnancy. Oh wells. I'm at 40 Weeks 6 days now, and still waiting since my amniotic fluid is sufficient, and baby is active. I'll be induced tomorrow night at 41 weeks, if baby still doesn't arrive by then. Contractions only started to be more frequent (7 to 10 min apart) for me after Week 40 and 4 days. At Week 40, I was only 1 cm dilated. So it really differs for people. Just listen to your gynae, and if it is safe for you and baby, it is fine to wait.
Pregnant women tend to have constipation more at the 3rd tri so try to take more fluids & eat fruits. Hard tools are difficult to pass so you need more fluids or try to drink milk. I know milk helps. As for 1cm dilation, yes you won't feel any contractions or braxton hicks unless you're already 3-4cm dilated. It is very normal to be dilated at 1cm when you have your cervical check. If this is your first pregnancy, you will definitely need an episiotomy unless you have had other pregnancies before. I only needed episiotomy for my 1st and don't need any for my other 3.
I think you can ask gynae to give you other medicine to soften your stool. Importantly try to relax and think of baby more than the process of getting baby out. Wishing you smooth and safe delivery 😉
I had piles nearing edd.. but after delivering my baby (had episiotomy), I have no difficulty to poop with lactulose.
https://sg.theasianparent.com/severe-pain-from-constipation-during-pregnancy
I had piles at 3rd Tri