Thanks for your comments, everyone.
I cut the sleeves off and cut up the sides of the original shirt. Then I just laid it flat and used the body of the shirt as if it were yardage, lining up the neckline of the pattern piece with the button placket. I slid the sleeve pattern piece down the shirt sleeve to the place where the width was right and cut the new sleeve top there so it would fit in the new shoulder. After I put the front of the shirt together, I cut the back piece to match the length of the front (shorter than the pattern indicated) so I could use the original shirt hem.
Hope this helps. Let me know if you have any more questions.
P.S. Don't forget to eliminate the seam allowances where you won't be needing them. In this case: the sleeve seam and the center front where a facing would have gone.