Sculthorpe was suspended by the Wildcats last week for a breach of club discipline and has now left the club whom he joined in 2007.
Fellow prop Korkidas has struggled to make an impact at any club since leaving Wakefield in 2006, playing for Salford in 2007, Castleford in 2008 and Huddersfield in 2009.
The 28-year-old signed a three year deal with the Giants at the start of the season but has failed to break in to the first team under new coach Nathan Brown.
Wildcats Head Coach John Kear said: “We are delighted that Michael will be returning to the club, he was here when I first joined the club and he was sad to leave back then, so we are delighted to have signed him for the rest of the season and look forward to getting him back into a Wildcats shirt.”
Giants Head Coach Nathan Brown said: “We are really pleased for Michael that this opportunity has cropped up for him in first grade as its where its best for him to be playing week in week out.
“Danny Sculthorpe offers us different traits in the front row to what we have already got and whilst its sad to see Korky move on as he is very popular here with everyone it will, I am sure, benefit both clubs and both players.”
Sculthorpe meanwhile will make Huddersfield his eighth club, having played for Leeds, Warrington, Rochdale, Wigan and Castleford before his spell at Wakefield.