I'm not sure if the Cowboys really have many more injuries after signing that most other teams in the league, its just part of the game. Maybe they do, I just dont have any actual numbers to support it either way. Where the Cowboys struggle is in that they do often wait until the last minute to sign a player which can make it more difficult to get out of these deal when injury occurs. It depends on the structure of the contract and how the guarantees are laid out, but typically signing early makes it easier to cut a player if problems pop up and you save a little bit on annual value on the deal to help lower that dead cap number if it comes to that. The DLaw contract comes to mind where they hit him with the franchise tag for two years then signed him to top money on a 5 year extension after that. Same situation with Dak. The older a player is the more likely they are to get hurt, and the longer you wait the more the cap goes up resulting in a higher AAV to extend these guys.
The other issue the Cowboys run into is that they have no problems extending players who have an injury history, or are recently injured. Jerry also loves gambling on a player who falls in the draft due to injury.