Wilde, who joined the Shaymen at the start of the 2016/17 season under former boss Billy Heath, made seventy-two starts, scoring 3 goals.
But he, along with Tom Nicholson, Martin Riley, Cliff Moyo, Danny Clarke and Tom Denton are all leaving The Shay.
Town boss Jamie Fullarton has Sam Johnson, Matty Brown, Scott Garner, Matt Kosylo, Jake Hibbs and Michael Collins already under contract for next season, while the club has confirmed that Sam Graham has been recalled by his parent club Sheffield United.
Discussions are ongoing with the remainder of the squad.