Holy cow, with 3 under 5 that I take everywhere with me, I say 'no' 10,000 times on a grocery store trip alone! No does not mean "I hate you, you're a bad person". I think that theory is from the shrinks with their own baggage.
So with the assumption that you need to use the positive phrase rather than the negative for stuff...like instead of saying "No" when my 3 yo wants to dash down an aisle pushing the cart with my 2 year old in it, I would say, "Let's leave the cart right where it is instead" to spare him the "no". Fine. Multiply that by a million things per day, and I ain't got that kind of time. Plus its too wordy for toddlers who have tiny attention spans. My kids stop on a dime when they hear "no" and they are happy exuberant confident kids.
Sure, you don't want to say "no" to your older child's dreams and aspirations, but when your toddler is across a large restaurant and about to dump their piece of birthday cake on a friend's head, I say, yell "NOOOOOO!" and don't feel bad.
The catch is, for "no" to matter, it needs a consequence to go with it at first for it to become an effective warning, otherwise you're just pointlessly saying it all the time, but lots of people don't like disciplining at this age. I did though and it saved me a world of trouble later. But regardless, you should at least teach "no". It just means "stop that immediately" which comes in haaaandy.
We have friends who protected their daughter from "no" and never said "no" to her...and she acted accordingly-still does at age 8, no one can tell her no, that's for sure. She can't handle it. It's not pretty.