Just a thought on the trains, go to South Parkway, not Hunts Cross, and get a bus to the airport from there. That is how Merseytravel want passengers to go. But from the Swan, a bus is better, saves you getting into town and back out.
There's a great route to cycle to the airport if you've got a bike, offroad nearly all the way. Look up 'Liverpool loop line', or if you turn cycling on in google maps, you can see it. Its an old railway line thats been turned into a (tarmacked) bike path. Runs past Old Swan and all the way to Hunts cross, then follow the transpennine signs into Speke and just cut across to the airport.