Good luck. Wife and I took our walking 10 month old to Hawaii this past May. Flew F with his own seat and car seat. I think that's the key, if they can get their own seat, do it. It was worth the extra $1500 to us for him to be comfortable and me to be comfortable not having to hold a squirming baby. Can you "wear" either one through the airport? We did that and carried his car seat and checked his stroller, since gate checking and waiting for the stroller sounded horrible.
This probably doesn't help you much, but once again, good luck, and don't worry about other travelers. I almost ruined our trip because I was sorry worried about him crying and what other pax might think or give us the stink eye. 99.5% of travelers are forgiving and probably would be willing to help if you needed it.