When translated literally, the Japanese lyrics for the original songs seem a little dry to me, so I think the localization was fine for what it did. “A New Day is Dawning” is I think the best of the three, however. “Swim This Way” is just flat-out cringy in English.

Ex - “Swim This Way”

ENG:

“Swim this way We'll dance and we'll play, now It's very easy, come on in Just take a chance and shake a fin.“

JP (Pardon any translation errors, I’m a beginner in the language):

“Now, let’s dance. (さあ、踊ろう。) Now, let’s swim. (さあ、泳ごう。) Anyone can do it. (誰でもできるよ。) [It’s a] fun musical.” (楽しいミュージカル。)