score:5
but both of them seem to want US phone numbers
Uber and Lyft don't require you to have a US number when you register. Any international number that can receive a text message is going to work. There might be an issue with US drivers not wanting to call a foreign number in case they can't find you, but otherwise it doesn't matter which country you're coming from.
Is it possible to use either of these services purely via the internet (depending on airport wifi)?
If you have a smart phone it's possible to use the service through WiFi. Once you get into the car you no longer need to stay connected.
: I don't have a smart phone, so this would all be using my laptop's web browser (not the actual app)
Normally the apps require you to run them on a smartphone. You might be able to run it on an emulator though, but I've never tried it.