I'm a little confused. If, for example, a man is singing a song written by a woman, and it has ending particles such a "の" "なの" etc. What are the male equivalent of these, or which ones are to be omitted? Or do you leave them?
As far as lyrics are concerned, in the Japanese culture, the original lyrics are never modified even when they are sung by someone of the opposite sex. If the original lyrics say わよ, a male singer sing them as わよ. That's not strange at all, and no one thinks he is gay. (In English-speaking cultures, this may not be true. You can see "his" changed to "her", and so on.)
Traditionally, Japanese singers have made and sung many songs completely from the perspective of the opposite sex, using words of the opposite sex. Famous ones include 女のみち, 心凍らせて and 舟歌. (Note that these are not "covers". The guy with mustache in the first video wrote 女のみち by himself, sang it by himself, and sold over 4 million copies.)
Outside lyrics, feminine の can be changed to よ/さ/ぜ/etc, and feminine なの can be changed to だよ/さ/だぜ/etc. For example, 手を繋いだの → 繋いだよ/繋いださ/繋いだぜ, 好きなの → 好きだよ/好きさ/好きだぜ. Again, don't do this in a karaoke room. It's funny at least, and some people would feel it's disrespectful and offensive.