I did wonder if I could try do this. However they are often red face crying/screaming which alerts me to her nappy needing changing and i can’t see myself leaving them long enough to let the poo happen. The poo happens once they are on the changing mat, baby is relaxed and then the poo just happens without warning. So it’s a tough one to sort.
Have you tried bicycles and other gentle tummy massage to help baby to poop? My baby was a bit like this when newborn not every poop but I would change her nappy and just the motion of bending legs/ legs over tum would make her poop in the fresh nappy or have an accident on the mat. Try doing the massage before you change nappy after the wee and see if that helps? Also incorporate tummy massage as part of bedtime routine with a gentle oil. At 4 weeks babies are still only just learning how to wee and poo so this won't last forever. Sometimes the just need a little help. I was the same as you paranoid about going out incase baby had a poonami. But it does get better!
Take the diaper off and hold her over something you are okay with her pooping on. Elimination communication might work really well for her. Puppy potty training mats are also great for controlling and catching baby poop messes.
I second puppy training mats, take them with you everywhere, and also spare change of clothes etc because if a poonami does happen then you’re prepared. I was nervous to go out too with my LO but the only way to get used to it is to just do it , the more you do it the more comfortable you get. Honestly I don’t think twice now about taking my LO out, we just go, and are out all days. Just make sure you pack the correct things x
Can you leave it a while after a wee to change.