I don’t think you should use ~しちゃった in polite speech. It has a shade of currying sb’s favor and may sound feminine, but not so much, males often use it, too. Rather, I think it sounds childish to some extent.
A man would say
遅れたけど来ないよりましだろ(う)?
If polite
遅れてしまいましたが、来ないよりはいいですよね?
But I want to argue that besides excusing, saying 来ないよりいい sounds arrogant if not rude. If you’re in a formal situation, you should excuse for being late anyway.
遅れて(しまって)申し訳ありません〔すみません〕。
Though it depends. I can't speak of others.
