Get the epidural if you wish, or if you need it, but please educate yourself on its risks to yourself and your baby (and yes, they do exist) so that you won’t have to say later “How come nobody TOLD me I could have an epidural headache for days/weeks” or “How come nobody TOLD me that my baby could be too sleepy to nurse due to the anaesthetic being passed to him during labor?” It’s true, the chances are that it will be fine, and there will be no aftereffects. But they can happen, so educate yourself.
Have a backup plan in case an epidural is not available (it happens), cannot be placed successfully (it happens), simply doesn’t work (it happens) or only works on one side (you got it.) Have plans in place for how you will cope with labor pain - relaxation, hot water bottles, labor ball, hypnobirthing, and a really good labor support person. I recommend a doula very strongly. They’re trained to support you, and a professional support person who is there for you and your husband, who doesn’t have to do other, hospital-related things, and who furthermore will help you remember what your wishes are for the birth when your brain has shut down and you may be being pressured to accept things you didn’t want simply because it’s policy… is worth her weight in gold.
Dilation is irrelevent. Seriously.* But allowing your doctor to strip your membranes may lead - as it did in my first pregnancy - to an “accidental” rupture of membranes, which means you are abruptly and unexpectedly “on the clock”, with the increased risk of infection that comes with AROM, and the increased risk of surgical birth that comes with induced/augmented labors that do not start spontaneously. Go ahead with membrane-stripping if you understand and accept this possible outcome.
*I was at 4cm for weeks with my firstborn, with prodromal labor (1 contraction every 7 minutes by the clock for weeks). My best friend was at 8cm for a week. Mind you, when she finally went into labor, it was a very short labor! My OB told me of a woman who came in for her 40 week checkup, no contractions at all…at 10cm. They took her up to L&D, broke her water, and told her to push. Shortly thereafter she had a baby in her arms and she NEVER had a contraction. Every OB has seen women they’d swear is going to delivery within 24 hours, who goes another week or two, and women whose cervixes are high, tight and closed at their appointments, who deliver that evening. You just never know. (But probably, you’ll get to experience plenty of labor before your kiddo is born.)
Please don’t let anybody tell you “if you’re at 4cm, you are in labor” (as happened to me, leading to “augmentation”, which led to “failure” of my labor, which led to cesarean section). It is true, most women are in labor at 4cm. But you might be an exception - relax! Your body knows what it’s doing! Every woman deserves to be seen, and treated, as an individual - not as an average, not as a statistic, and certainly not using a one-size-fits-all policy.