The group, formed on ITV1 show "Popstars" in 2002, has had eight top-five hits.
However, the five Girls Aloud members were angered Walsh planned to disband the group after their next album to launch Nadine Coyle as a solo act, Sky News reported.
"I have absolutely no intention of leaving the girls and going solo," Coyle said on the group's Web site. "What sane person is going to leave the biggest girl band in the country?"
The group has hired Shaw to handle day-to-day management, Heat magazine reported.
Walsh, who is busy with other projects, said he is happy with his co-manager role.