I walk my hyper dog and the buggy all the time, I just hold her with my righthand and push the buggy at sametime, only have to take my hand off the buggy to give the odd tug on the lead, you will manage fine. Just remember to put brake on buggy when picking up poo etc.
I always tie a nappy bag onto the lead so no rooting about when needed good luck and you’ll be fine, think your over thinking things 😉
Day 1 over, not too bad with the walks but no runs off the lead. I feel sorry for the dog as my kids haven’t stopped yanking out of her ears and trying to sit on her, she’s a lovely thing but counting the days til I give her back!!