I'd like to have my beard shaved, but I don't need to have my hair shampooed.
この場合、次のような言い方ができますよ。
ーI'd like to have my beard shaved, but I don't need to have my hair shampooed.
「髭は剃ってもらいたいですが、シャンプーは結構です」
to have one's beard shaved「髭を剃ってもらう」
to have one's hair shampooed「髪を洗ってもらう」
ご参考まで!