I JUST installed it on my Late 2010 MBA, 4 GB of Ram, 1.86 Intel Core 2 Duo, for the New Year AND so far so good. Not a issue with Safari, watching YouTube Vids, and other pass-time vids on sites I have an iPhone 5s and so far, zero problems on either end. Mail, Contacts, FaceTime, Messages, ALL check.
IF I was in your shoe, I would get a used Mac via Apple Online store and go from there as your Mac seems to be on the borderline.
IF I was in your shoe, I would get a used Mac via Apple Online store and go from there as your Mac seems to be on the borderline.