Hi Atreides. I've missed the postings by yourself, Hashchu, and Shumai. Hope you are all well and that your shoulder heals quickly.
I don't think core strengthening will improve your swimming balance much. Swimming is so much more complex than the exercises on that vid. You might want to try the super-slow swimming I've been working on. It challenges your balance in all phases of your stroke, its difficult, and its working for me. I really feel it in my core the next day, too. Twofer!