My guess is that male alters in a female body would not alter hormone levels. Transgendered alters are only a psychological construct, and not a physical reality. Physiological changes can change between alters, but I would guess these changes are a result of stress hormones and muscle tension rather than anything else.
Hirsuitism is not uncommon in women, and is a hormonal condition. It's causes can be varied, and it can be treated according to its base cause.