"It won't hurt to do too much"とは「やり過ぎても害はない」と訳せます。
Example sentence in context:
"In order to protect oneself from getting infected with covid-19, it's better to wash one's hands too much, rather than to do too little of it."
ーThere is no harm in washing your hands too much.
「手を洗いすぎても害はない。」
この場合は there is no harm in 動詞のing too much を使って表現できると思います。
ーNothing bad can come of being too careful.
「気をつけるに越したことはない。」
Nothing bad can come of being too ~ を使って「〜しすぎても損はない」を表現できると思います。
ご参考まで!