Check the user guide for the car seat. It should have a section for securing with just a lap belt. It should not be a problem if you get the belt through the correct slot.
This. My wife and I have two carseats for our 2yo. One for the car, big and heavy with a significant base. Cost way too much, but nice. It's tied into the car with LATCH and rear-facing, and basically never leaves. We've never used it in the plane. It has a complicated system for using a belt and I can never get it right. It's also very tight, so the times where the buckle ends up in the middle (often) it's near impossible to secure.
And then we have the cheap seat. Lightest thing we could find, we can carry it with one finger. It was bought for the plane. Huge holes for the belt (very important in a plane!) so that I can run my whole forearm through the gap and thread the belt. Then it's just a matter of adjust the belt tight and out from under the baby's butt. Let me ask my wife what model it was. Cosco something, I think and only like $40.
We've used it both forward and rear facing. It's solid either way if you cinch down the belt. We've used it in a (a) 172, (b) Cherokee, (c) M20, (d) 172RG, (e) Arrow, (f) Cherokee Six. The only plane that has ever given us trouble is the restart 172S with the crazy long buckles (which is, ironically, what I own now). Still workable, just isn't as easy. Because the belts are not generally inertia reel, you don't need the immobilizing clip.
All the seats that say FAA and DOT meet the same standard. Really the only difference is comfort and features, not safety. This seat works great for us, and beats lugging around the heavy, nice seat.
