"while wanting" is correct and usable in written English.
You can use it to indicate a desire that someone has in the present moment, and also refer to a desire that is ongoing. For example: "She sings while wanting to become a famous artist."
Winnie Foster talks to a toad in the road about wanting to be alone for a while, wanting to be unsupervised.
Real self-love is about remembering the bigger picture of who you are -- you are the Universe, expressing itself as a human for a little while, wanting to grow and expand through you.
I went on stage and introduced each act while wanting to hug the audience".
In the meantime, while wanting to try things and learn more, we should all proceed cautiously.
But I'm afraid the C.F.D.A., while wanting to act like a family, really represents individuals with very different interests.
While wanting a say in national policy, the Communists are necessarily antagonistic towards Congress, their main opponent in the states.
While wanting to help her son, Becky also wonders whether she lacks the imagination necessary to understand him.
"But I got the clear sense that Cirque, while wanting a different sort of show, also didn't want a show that looked too much like Broadway".
What could be more human than wanting to be seen while not wanting to be snooped on, or wanting to connect while wanting to be autonomous?
(Margalit Fox's obituary of John Fairfax) D. "… reason is only reason and satisfies only man's reasoning capacity, while wanting is a manifestation of the whole of life.
The prime minister will also be aware that India, the regional superpower, while wanting peace in Sri Lanka, does not want it at any price.
