The word you're after is "agender". So, pretty close. The answer is - whatever they tell you to. Some would prefer "they". Others wouldn't care if you use "him

The word you're after is "agender". So, pretty close. The answer is - whatever they tell you to. Some would prefer "they". Others wouldn't care if you use "him" or "her". Yet others prefer some invented pronoun (there's a long list). The only one that's likely to be inappropriate is "it". Don't use that.