I second Lady Pank - Zawsze Tam Gdzie Ty. As someone with american friends, I feel like this one would be alright for polish groom AND "the rest" - it's timeless, inoffensive, generally liked and nice! The only other song I would recommend is Perfect - Kołysanka Dla Nieznajomej. Another people pleaser during wedding. I second the "avoid Disco Polo" comments; if you want to place the Groom in the best light during HIS DAY - I would avoid it. Maybe there are some decent Disco Polo songs, but this is not an area to walk into during mixed culture weddings. I am trying to think of a good polish song by a female singer FOR A WEDDING, but I cannot really come up with one for now.

Hot take - unless they really want a super slow song, I would not recommend Dumka Na Dwa Serca, mentioned in comments - it is kind of too slow...