According to a statement made by The Catholic Medical Association in November of 2000, gay conversion therapy is considered a corporeal work of mercy.
This statement clearly points out that Catholic therapists are obligated to encourage chastity in all situations. The Church has always taught (and will always teach) that chaste behavior is required for spiritual health and well-being.
It should be pointed out that Catholics cannot support forms of
therapy which encourage the patients to replace one form of sexual sin
with another. (Schwartz 1984) Some therapists, for example, do not
consider a patient "cured" until he can comfortably engage in sexual
activity with the other sex, even if the patient is not married.
(Masters 1979) Others encouraged patients to masturbate using
other-sex imagery. (Blitch 1972; Conrad 1976) Catholic therapists
working with Catholic individuals should feel free to use the wealth
of Catholic spirituality in this healing process. Those with father
wounds can be encouraged to develop their relationship with God as a
loving father. Those who were rejected or ridiculed by peers as
youngsters can meditate upon the Jesus as brother, friend, and
protector. Those who feel unmothered can turn to Mary for comfort.
(Homosexuality and Hope, part I, sect. 5-6)
As you pointed out, the CCC is clear about the chastity of those afflicted with same-sex attraction:
Homosexual persons are called to chastity. By the virtues of
self-mastery that teach them inner freedom, at times by the support of
disinterested friendship, by prayer and sacramental grace, they can
and should gradually and resolutely approach Christian perfection.
The Church, as well as the CMA, teaches that anyone with any type of sexual disorder (i.e. masturbation, adultery, homosexuality etc.) should be approached with nondiscriminatory therapeutic charity. Where ever mercy is needed, the Body of Christ should be there.
The teachings of the Catholic Church on sexual morality are explicitly
clear and do not allow exceptions. Catholics have a right to know the
truth and those working with or for Catholic institutions have an
obligation to clearly enunciate that truth. Catholics must, of
course, reach out to individuals experiencing same-sex attraction, to
those actively involved in homosexual acts, and particularly to those
suffering from sexually transmitted diseases, with love, hope, and the
authentic, uncompromised message of freedom from sin through Jesus
Christ. (Homosexuality and Hope, part I, sect. 5-6)
History has shown that whenever the Church makes a counter-cultural stand to defend her morals, she is always met with opposition. This sometimes puts a heavy burden on those providing medical and psychological treatment. Nevertheless, the Church stays true to the Law of Christ, which is the Law of Merciful Love. Catholic physicians and therapists are obligated to do the same.
While any attempt to teach the sinfulness of illicit homosexual
behavior may be greeted with accusations of 'homophobia', the reality
is that Christ calls all to chastity in keeping with the particular
state of life. The desire of the Church to help all live chastely is
not a blanket condemnation of any who find chastity difficult but
rather the compassionate response of a Church seeking to imitate
Christ, the Good Shepherd.