What is the behavior of a Zwitterion during ion exchange chromatography?
I would expect it to depend on the pH of the mobile phase. The charge of your stationary phase and whether you want the azide to elute will determine what charge you want on the azide. Given that, you should set the pH of the mobile phase either acidic or basic enough to ensure that the azide is fully charged in the direction that you want.

From Wikipedia:


  Proteins have numerous functional groups that can have both positive and negative charges. Ion exchange chromatography separates proteins according to their net charge, which is dependent on the composition of the mobile phase. By adjusting the pH or the ionic concentration of the mobile phase, various protein molecules can be separated. For example, if a protein has a net positive charge at pH 7, then it will bind to a column of  negatively-charged beads, whereas a negatively charged protein would not. By changing the pH so that the net charge on the protein is negative, it too will be eluted.


If changing the pH is problematic, apparently increasing the ionic strength can help shield the azide's charge from the column's charge:


  Elution by changing the ionic strength of the mobile phase is a more subtle effect - it works as ions from the mobile phase will interact with the immobilized ions in preference over those on the stationary phase. This "shields" the stationary phase from the protein, (and vice versa) and allows the protein to elute.