As if the person is an excellent mediator, not whether he or she was a good judge or a good litigator. Some mediators are more evaluative than others. Be candid with yourself and the mediator about what sort of process you want. You are, after all, paying for it. Good mediators have a range of styles, just as good litigators do.
Some styles are better for some disputes than others.
Too much is made of expertise. There grew up in international arbitration a cadre of people in each major geographic center and within each vendor of arbitration services a network of candidates to resolve your dispute. Risk aversion, if nothing else, suggested a level of comfort with the tried. You might wish to consider other practitioners if they can bring you the most important virtues a mediator can bring to the conflict, especially imagination. Find people within your organization who have creativity.