With Thompson sitting out tomorrow's match with a toe injury, Shillington said 24-year-old second-rower Edwards was the man to step up in his place.
"Edwards has shown he loves to put his shoulder in there and get aggressive in his defence, so he'll be a perfect match up there on Toddy," he said.
"I think that will be the key to bringing him down, having that edge defender putting a fair bit of pressure on him."
However, Shillington emphasised that their approach to Carney in defence wouldn't be the area where the game was won or lost, with in-form Sharks forwards Luke Lewis and Andrew Fifita also standing in their way.
"We've got to start with the forward pack," he said. "It's not just about shutting down Toddy Carney - we take down the forward pack first, hopefully."
Meanwhile, Cronulla chairman Glenn Coleman has quit the embattled NRL club after just two months in the job. Former Olympian Damian Keogh is expected to take his spot.
Coleman took over from predecessor Damian Irvine, who stepped-down in the midst of ASADA's investigation into drugs in sport.
Coleman was left as the only director not aligned with the Sharks Unity ticket - headed by three-time Olympian and former Sydney Kings basketballer Keogh - whose group swept to power in recent board elections.
He remained unchallenged as chairman but had differing views to the new board. He said he was leaving to allow the new board of directors to lead the club.
Coleman, who played 123 first-grade games for Cronulla, said he was happy to step back and concentrate on his business.
The new board is expected to ratify Keogh as chairman next week and appoint a new director in his place.
Cronulla are having an inconsistent 2013 season with the ASADA investigation proving a constant distraction to the players and officials.
- AAP