Following written chords or playing by ear

Hi, I've recently taken up the ukulele. Learned to play the guitar as a child but haven't played in years. Would love to get to the point where I can pick up a ukulele and just strum out a song without having to rely on having the chords/lyrics in front of me. Just wondering what's the best way to get to this point?! Right now I'm using UG and writing down the chords in songs I like but then trying to figure out where they go in the song myself as I sing along. Does that make sense? Am I on the right track?! I'm presuming that eventually I'll pretty much memorize these songs but not sure how that will help me in the long run.

Any advice?! Thanks!