I went to DisneyWorld on P1 and while it wasn't always fun to just not indulge, I found it relatively easy. I brought lots of packets (mostly RTD shakes - packed in my luggage - and Quest bars) that were portable and I could throw in the backpack. If you are walking a lot, I would add an extra packet.
We stayed on-site but did have a small fridge and I ordered groceries before hand that were delivered right to our hotel so I could also bring veggies with me. It was pretty easy to eat a P1 meal at dinner - usually chicken and veg and salad.
You do miss out on the Disney treats but I knew they would make my stomach feel rotten anyways so I focused on enjoying my kids and husband enjoying them. I also took a water bottle and it was easy to fill it at water fountains.
A mantra I have learned on this site is that with planning, you can truly do anything. You will be able to pull off P1 at Disney and have fun!