You won't need the base when you're traveling. The SnugRide is designed to be installed by itself, just make sure you read the instruction manual (and/or the side of the car seat) and practice before you go. I did the same when traveling in Europe. The base is just designed to make life easier when you're going to be putting the car seat in the same car(s) all the time. But it is simple to install the car seat without it. If the seatbelt in the taxi isn't the kind that locks and stays tight, you'll have to use the locking clip that is snapped into the back side of the car seat. It's easy to use.
You are exactly right to just bring just the car seat, Snap 'n Go and Baby Bjorn -- that's exactly what I did and it worked out great. No need for a big, bulky stroller when you travel.
It will take you a minute to install/uninstall the seat every time but it is worth it for the peace of mind.
Have a great trip!