If you don't want to bring them, then book yourself on the Grayline Disneyland Express. It's a coach bus, so there are no seatbelts at all.
But if you're taking a cab or shuttle, you'll need them. I doubt the drivers will MAKE YOU, but if for some reason the shuttle is pulled over, I'm guessing it will be YOU that gets that ticket, and if there's an accident, well, I won't go on except to say...the way the SS drivers drive, I'm surprised there aren't MORE SS accidents.
We've gate-checked our Nautilus (DS is 5 and will be in a 5 point harness until he's too big for any 5 point harnesses out there) or previous seats with Southwest, Virgin America, and Jet Blue, no problems. For some reason some xray machines can deal with the Nautilus just fine (seatac and lax) but others are smaller (San Diego).
We baggage-checked our seat once, but later I watched the boosters and seats come crashing down...and I realized I would never willingly do that again. The impacts with the baggage carousel were so strong it almost made me go and replace my seat...ugh.
Anyway, it's easier to just go on a coach bus, so book Grayline Disneyland Express.