SnowflakeMum - when we travelled to the US, I emailed all manner of "important people" (can't remember exactly who they were but along the lines of US road safety organistions; state law people etc...) and they told me that unless the car seat has a sticker that specifically says it complies with US law (or words to that effect) then it isn't legal to use it. I may still have the emails if you'd like me to have a look and forward them to you.
After much googling, I found out that allegedly EU regulations are stricter than US ones in terms of safety - so whilst UK car seats may not be legal, IF they were to be safety tested in the US then they would be pretty much guaranteed to pass due to being made to stricter standards. I know that's kind of irrelevant in terms of the legalities, but at least it meant that it would be safe.
I worked myself up into quite a state over it as I just couldn't work out what to do for the best. In the end we decided to buy a 2nd UK car seat and take it with us, despite being armed with the above information. Our car hire company wouldn't guarantee that they would have one available, and said that even if there was one available, they didn't provide instructions as to how to fit it. I figured that the last thing we needed after a 10 hour flight was to try and figure out how to fit a strange seat and probably end up doing it wrongly! So it was kind of a toss-up between 'safe but illegal', or 'legal but potentially unsafe'. By taking our own at least we knew that we had one which had to be better than getting there and finding there wasn't one!
I think it's a very good idea to pick one up over there if you can (they are SO cheap), and if you were to get a new one it would come with instuctions obviously, although as you say, it does pose a problem as to how to get from the airport to the town. Would it be an option to take the cheap one you bought to use from the airport to the town and then buy another one at the first opportunity? Or would that be car seat overload?
Good luck, these things are never simple are they?