My own approach has always been to get my fingers in the right place, strum that chord ONCE and sing the words that chord covers, then as I get to the next chord, I stop singing, place fingers, strum ONCE and sing the words THAT chord covers. I work through a verse like that and keep working at it until I can switch to the next chord smoothly and I don’t have to stop singing. Sometimes I start working with the Chorus of the song first. The main thing is patience! And don’t work HOURS on the same section. That will get you frustrated quickly. I like to do just a little at a time and then work on another song for a while.
Seems to have worked okay for me. I hope you can say it works for you! Best wishes.