Well ... I don't have a Shape Shifter, but maybe I can help you out anyway...
The TT web site says the SS expanded external dimensions are 20 x 12.5 x 7"
The last plane I flew on had a 22 x 14 x 9" limit for carry-ons ... your bag meets that dimensionally OK.
I normally fly with a roller bag that is 9" thick, and it easily goes under the seat in front of me and is 17.5 x 13" in the other dimensions. I would think your only problem with putting it under the seat is the 20" height ... it might stick out too far and attract attention of the flight attendants. If your seat-mate didn't have a bag as well, you could probably rotate the bag sideways and slide it under, but it would take up more than your share of the space.
Thus, you will probably have no issues getting on the plane with the bag, and you might be able to travel with it under the seat in front of you, but if you get an over-zelous attendant, you may be asked to put it into the overhead bin on some flights.
Hope that helps...
-howard
I found a note that CRJ-200 regional jets have dimensions of:
Overhead Bin 18 x 14 x 7
Under Seat 19 x 15 x 11