We went stroller-less for our first trip. Our son was a new five, and our daughter was 7. They did great, no whining, no complaining.
We took a swim break at midday and had a sit-down meal each evening, both of which probably helped a lot.
The only time I remember holding/'carrying them:
We put them on our shoulders in an outdoor line because they were sweating something awful down there in the crush between people. We were cool enough, but they definitely were feeling the heat. It helped them catch a little breeze, and took their mind off how hot they were. (Might have been the Indy cars??, I know we were in that part of MK.)
We also put them on our shoulders in the very back row (standing) for Fantasmic. They were too short to see otherwise.
DS did poop out one night at MK while waiting for the fireworks. DH held him through the show, out to the buses, standing for the bus ride home, and back to our room. Really, we could have woken him and I'm sure he'd have walked, DH just didn't see the need to.
My sister took my advice and left the stroller at home, and just rent as needed when her sons were 4 and 5. She did end up renting during their Epcot day. But, they never took breaks and only did counter service meals, so they were on their feet all day in that huge park. She enjoyed the freedom of not dealing with the stroller during the rest of their week.
I think you should go for it, but be open to changing your plan if it doesn't work out! Good Luck!
ETA: Be sure to watch for blisters forming on your kids feet. They aren't as bad as us old folks, but it can still happen, and I can guarantee they'll be whining about that. Mole Skin is a great product if you feel a hot spot forming. It sticks well and keeps the area safe from rubbing, much better than a band aid. Mine is safely tucked away in my bag, just in case.