well. if you wanted to. you could use the credits shown in the opening. If you wanted to list both, then maybe use Chris Kirk as Chip Skylark or something. I think it's reasonable enough anyways. I also don't really see any harm in just using Chris. Depends how correct you'd want to be.

There's also this in the credits below. Note the song is all capitalized. So yeah.... =/

I'm assuming these are the people who wrote the song. Probably should put them in the tags.
Not much else I can help you with here. I did a little browsing and came up with nothing. No official writing/soundtracks like you mentioned.
I was using this as a reference to everything above.
That's all I can really do to help. Sorry it isn't an actual answer.
There's also this in the credits below. Note the song is all capitalized. So yeah.... =/
I'm assuming these are the people who wrote the song. Probably should put them in the tags.
Not much else I can help you with here. I did a little browsing and came up with nothing. No official writing/soundtracks like you mentioned.
I was using this as a reference to everything above.
That's all I can really do to help. Sorry it isn't an actual answer.