I think a good thing you'd want to try would be not only trying to sing a song, but taking a song sung by a female singer, listening to it carefully and trying to imitate the sounds she makes, not the song itself; trying to copy aspects of her voice.
It's also very useful, I think, to try to imitate as well as possible voice actresses. Not actresses - voice actresses. Because actors are into their role and all, while voice actors focus on voice only. It's always clear and just as intended.
And you're going to want to focus on the sound, again, here. Not the sentences. When you hear your own language, you'll naturally tend to focus on the meaning much more than the voice, and miss things even if you try to focus on the voice. So a foreign language it is. And it's good for songs as well. If it's a foreign language, you won't even understand most of what you'll be singing. So you'll be focusing much more on how it sounds.
Where are there many voice actresses in a foreign language? Japanese anime! I used to do that, sometimes. I would watch an episode, and at some point I'd hear something that sounds good. I'd pause and try to imitate it, and rewind and listen again, and try again, until I got it somewhat right. Inoue Orihime's "Shinanaide, Kurosaki-kun!" from Bleach made me understand things. Just like that other Japanese song made me understand some other things. Once you understand something about a female aspect of voice and manage to reproduce it, integrating it in your everyday voice is much easier
