If the pronoun's gonna be int'l, then ch is impossible because many languages (e.g. Hawai'ian, Latin, Arapaho, etc.) have neither a ch, an sh, or a tsh (tsh makes the sames sound as ch).
If it weren't int'l though, then "the" would be the most logical choice. It would be pronounced with a th like in "with" and an e like in "he". It would be "the" because "the" is the Greek root that means god/deity. A sexless deity would be "thit", a male deity would be "the", and a female deity would be "theem".
He/him/his, she/her/her, and it/it/its would be the/thim/this, theem/ther/ther, and thit/thit/thits, respectively. "Thit" does not refer to an object, but to a sexless deity, like the Christian/Hebrew/Muslim God (in some portrayals), or the FSM.