Getting to LGA isn't actually that bad. The NYC Century takes you on a route that goes around LGA, and there is easy access to Terminal A. Terminal C/D where Delta is wouldn't be too bad, I've seen airport employees walk in from the outside, crossing the same bridge the century uses to get over the highway. Terminal B is a mess right now due to the construction. For JFK, it is easy to get into the long term parking and then take the airtrain from there.
Would I do it myself? Nah.