For 22" you'd need to cast on 118sts or 22 fewer sts than the 140 the pattern calls for. You can take that out of the shadow rib if you want on each side. The rib is a multiple of 3 (actually 3+2) so if you drop out 9sts on each side out of the 35 given in the pattern you'll decrease a total of 18sts and you should still be within the 22-23" width that you'd like.
Cast on 122sts, follow the pattern and when you change to the larger needle (size 7 is used in the pattern but use whatever you have been using to get gauge) work 26sts shadow rib, k1, 10sts banjo, 48sts double, 10sts banjo, k1 26sts shadow rib.
Something to watch out for: The double cable is going to pull in the width of this sweater quite a bit. You could knit a swatch with your current needles in the double cable just to see what you get and factor that into the width measusrement. The double cable is done over 48sts so it will account for about a third of the cast on sts.
Good luck with this very handsome sweater pattern.