Cotterill got his recruitment up and running by bringing in Bristol Rovers left-back Luke Leahy on a free transfer before agreeing new contracts with Daniel Udoh and Matthew Pennington, who spent half of last season on loan.
Midfielder Edwards was part of the mass exodus this summer as the Pontesbury-born star was not offered a new contract, along with around a dozen other senior players.
But the hometown hero is confident that Cotterill's experience of 25 years in management, as well as that of head of recruitment Keith Burt and the contacts of assistant Aaron Wilbraham, who himself had over two decades in the game, will ensure Cotterill's rebuild is a successful one.
"The chairman – who is always excellent as a chairman in backing managers – I'm sure he'll back Steve Cotterill," Edwards said.
"There won't be many signings I think he'll get wrong. There's obviously always one or two that don't work out, but I genuinely think that, alongside Keith Burt who's with him, and the connections the gaffer and Alby's (Wilbraham's) got, they will assemble a very good squad for next season."
Cotterill is assembling his first Town squad after leading the side he inherited from Sam Ricketts partway through last season to League One safety.
It is understood that Shrewsbury have been actively busy in the market, sounding out several options while being ambitious in their pursuits. Their priority is in the forward ranks, while they are also on the hunt for a first-choice goalkeeper and at least one other option at wing-back.
One such ambitious link is that of out-of-contract Charlton frontman Chuks Eneke. It has been reported that Salop are prepared to match the 27-year-old's wages at The Valley in a bid to win the race for his signature.
The second new permanent signing of the summer, that of defender Pennington from Everton last week, is another signal of the club's lofty aims to compete for the play-off places next season under Cotterill.
Edwards feels that, despite his own situation, such a summer clearout was necessary at the Meadow as the manager puts his stamp on things.
"Looking back on it and taking my personally emotions out of it it is probably what needed to happen, in terms of him freeing up the budget and having players without the last few years' of baggage on their backs inside the football club," the Salop fans' favourite added.
"It was probably the right thing to do and he can really build a team which is his, rather than one he inherited."