Wade underwent an MRI on Monday, and it revealed the sprain of the medial collateral ligament.
Swayne is a longtime starter in the NFL, so having him in the starting lineup against the Jets isn't a concern. What is a concern is the backup situation.
Should anything happen to either Swayne or left tackle Spencer Folau against the Jets, the plan is to move left guard Mark Dixon to tackle, with Heath Irwin or rookie Troy Andrew stepping into Dixon's spot.
Wannstedt was even asked about the possibility of using tight end Hunter Goodwin, who was a tackle at Texas A&M, on the offensive line.
"Oh, to finish a ballgame, maybe," Wannstedt said. "We're having a tough time with not throwing him the ball. We don't want to say he's a right tackle."
With the offensive line situation, the Dolphins added guard Ray Redziniak to the practice squad on Tuesday, waiving linebacker Kevin Rollins to make room.
Redziniak, a three-year starter at Illinois, went to training camp with the New York Giants as an undrafted rookie free agent this summer and was waived on Aug. 27.