One great way to improve core strength while sitting is by using a stability ball instead of a chair. Sitting on a stability ball forces you to keep your core muscles engaged for balance and will build strength over time. As an extra bonus, you will burn more calories just sitting at your desk as you will move more throughout the day. Of course, this is not a magical cure all for being sedentary and it is still important to get up and move around. It also may be advisable to switch between a chair and the ball, especially at first, since your muscles will grow fatigued more quickly. Check out this link to see the proper way to sit on a stability ball.
So remember, the best thing you can do for your health is simply to move, but increasing your core strength is also very important! Isometric exercises, like the ones that you to do with the Wellshell all build core strength. For some great examples of core strengthening exercises check out: Core Strength Part 2: Core Exercises and the WellShell and Yoga Poses to Combat the Ill Effects of Sitting