I use 2 picking patterns in different sections of the song:
The finger-string assignment is:
In order to sound like the original, you will need a ukulele with a low G string.
The picking pattern is 1-2-3-2 (thumb - index - middle - thumb). This is pretty fast, so here's some tips for faster chord transitions.
Since you don't pick the A string, you can use a shortcut to make the D - Bm chord transition easier. To play the D chord, barre the entire 2nd fret with your index finger. This will give you the notes of a D major chord in the GCE strings. Then, to transition to Bm, all you have to do is press your ring finger down on the 4th fret of the G string. To transition back to D, release your ring finger from the 4th fret.
We can also make the chord transition between Em and A7 easier. Play Em with your middle finger on the E string, pinky finger on the C string, and ring finger on the G string (443x). Then, to transition to A7, all you have to do is press your index finger on the 2nd fret of the G string and release your ring finger from the 4th fret of the G string.2. Picking II - chorus
In the video, I wrote out the complete tab. It looks complicated, but if you focus on what the right hand is doing, you can break it down into 3 subcomponents.
Practice each subcomponent separately. Once you've learned a subcomponent, you can try playing through the entire chorus with just one subcomponent e.g (1234)-(234). Then, you can work on learning how to switch between these different picking patterns.