Sleeves with hems or simple sleeve bands are easily shortened. Sleeves with cuffs are another matter. The difficulty comes not so much with the cuff as with the sleeve opening. Begin by determining how much you want to shorten the sleeves. If the sleeve openings are deep enough, you may not need to change them.
Taking the Cuff Apart
Carefully remove the cuff by taking out the stitches that hold it to the sleeve. There may be topstitching that needs to be removed as well. Remove the binding or placket if necessary. If the opening is hemmed, you may not need to remove anything but the end dart and the top inch or so of the hem.
Cut off a little less of the bottom of the sleeve than your measurement suggests you should shorten it. Your seam will probably be deeper than what is left of the trimmed allowance. Plus you may have to take a deeper seam in the cuff itself, shortening the sleeves even further.
Fixing the Sleeve
Enlarge the opening in the sleeve if necessary. Finish the edges with the continuous lap or placket or by hemming. If you have trouble replacing the placket, see if you can't substitute a hem in its place.
Because sleeves are tapered, when you cut off the end, it will no longer fit the cuff. You will need to add a pleat or enlarge the existing pleats. Try to put them as close to their original position as possible.
Replace the Cuffs
Pin the cuff to the right side of the sleeve. You may need to take some stitches out of the ends of the cuff to be able to sew it on. Trim the shirt's allowance, finish the ends, and blind-stitch the underside of the cuff. Topstitch to match what was there originally.