When is a person obligated to divulge their status as a ger tzedek? Would a person working as a mashgiach need to volunteer this information if it wasn’t already asked?
There is no halachic restriction to the ger working at such a job, therefore there is no need to divulge this information. Personally, the fact that one is a ger is positive and not negative. In Hallel when we say “Yomar na yirei Hashem”… it is referring to geirim, (see Rokach, Megaleh Amukos, and others) who are considered the real yirei Hashem. One of the most crucial factors in getting a good mashgiach is that he be a yirei Hashem. Therefore, if you don’t want to say anything there is no need for you to do so.