Need advice from other Vocalists

Used to sing professionally for a short time in my 20's.

To just off the cuff improvise singing is a tough thing to do as there is no time to create lyrics on the fly.
You would be forced to limit yourself to vocals alone.

You could try harmonizing just tones 1&1/2 octaves high or lower than the lead guitar but you need to be able to harmonize perfectly and at best read the guitarists music sheets.

Or....

You could study someone more like what Bianca Antoinette does in Pink Floyd's Great Gig in the sky song.
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Or you could begin a lot earlier and bring back some kind of scatting like Ella Fitzgerald did, and if you did it really good your name could go down in history as the "new" lady of scat, since you would be bringing back a talent that is hard to do and almost a lost art.
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Maybe you can find your own way of vocalizing with no words to one of your band's tunes. Goodluck