"rather than wait" is correct and usable in written English.
You can use it to refer to an alternative to waiting. For example: "I decided to take the bus instead, rather than wait for a taxi."
Some left, rather than wait to be pushed out.
Rather than wait, Kouwe grabbed it from her site, she said Sorkin told her.
Rather than wait longer, Dr. Collins has decided that the government can start the work itself.
Rather than wait for rescue, he spent the next thirteen hours dragging himself to the surface.
But rather than wait for another sequel, regulators are pressing forward.
Rather than wait for their employees to cross paths, they could simply make the necessary introductions.
UBS's rivals should get on with it, rather than wait to be pushed.
He chose Honduras in April 2011, rather than wait to receive U.S. citizenship.
They are also more apt to attack an opponent immediately rather than wait.
Rather than wait around for the art world to catch up, Enwezor started a magazine.
