Whaley signed as an undrafted free agent in May. He started his college career at Texas as a running back before switching to the defensive line.
Briscoe was a sixth-round pick by Cincinnati in 2010 and landed on Tampa Bay's practice squad after getting released. He played in 18 games over two seasons with the Buccaneers and seven games with Washington in 2012 before spending last season on injured reserve.
Walker didn't play in 2012 after finishing his college career at Western Michigan. He signed with San Diego last year but was cut during the preseason.
The Cowboys open training camp Thursday.