McShane, 25, has penned a two-and-a-half year deal to move to the Tigers, while Moore joins Wakefield, his sixth Super League club, until the end of the season.
Wildcats chairman Michael Carter said: “With Paul signing for Castleford next year there was an opportunity to bring Scott here which suited all parties, and with the cooperation of the Castleford Tigers, we managed to get the deal done quickly.
“I wish Paul all the best for the future and look forward to seeing Scott in the red, white and blue.”
McShane had been an ever present for Wakefield in 2015 during a difficult campaign. He started his career with Leeds, making 63 appearances, and also spent time on loan at Hull and Widnes.
He said: “I’m really excited to join the Tigers and have the chance to help the club push towards a playoff spot in the Super League Super 8’s. I can’t wait to get started and meet everyone at the club.”
Moore, who moved to Castleford from London at the end of last season, adds Wakefield to his list of clubs which includes St Helens, Huddersfield and Widnes.