"Dave Button's a fantastic pro and is fine with it," caretaker boss Stuart Delaney told BBC Radio Shropshire.
"Jamie is very experienced, but understands I want to give young Tom Bradshaw the best chance to progress his career."
Delaney added: "Button's been first class, I can't fault him a bit. He's worked really hard with Chris Neal and [goalkeeping coach] Dave Timmins.
"He's done ever so well all season, and I'm sure he's going to have a great career in the game."
Striker Cureton, 34, was brought in late in the season from newly promoted Norwich to add to the Shrews attack, but failed to find the net in his time at the Prostar Stadium.
But Delaney, who replaced boss Paul Simpson to oversee Town's final two games of the season, has kept on-loan Huddersfield full-back Joe Skarz.
Source: BBC Sport
Source: BBC Sport