This is a very good question. After some thought, my opinion is that AW will only play for 10-20 mins per game for the first several games. This is not an injury where you suddenly are "cured" and are back to normal. Off the bat, I bet he takes 2-3 mins/game from CR and DD, and an additional 2-3 mins/game from DN, but I don't think we will even notice this decrease because it is so minimal.
I do not believe that TW, SS, TB, or SM, will take a hit because Warren does not fill the need in the positions they are playing. Once he is back to 25-30 mins/game, I think DN will take the most noticable hit...he has averaged 16.7 mins/game since he cracked the rotation 3 games ago. I bet he goes to 7-8 mins/game because AW will fill the perimeter shooting need that DN currently fills. EMc will also take a hit because I think instead of his 18 mins/game, we play SM at the 1 more and let DD handle the ball more often. DD is a better defensive player so keeping him on the floor is important. CR would be next just due to position conflict...not due to lack of performance.
Between DN, EMc, and CR, I think we find 25-30 minutes for AW...but we may be talking quite a bit later into the season. Again, just an uninformed opinion, take it for what it is worth.