I'm a ben Noach and was raised Catholic (and obviously left it). I'd just leave it be and only ask for prayers if the person is bnei Noach to some extent.
For instance, if they're religious in some other faith and pray, they'll just chalk it up to their belief system if the person gets better.
If they're bnei Noach then it is perfectly fine to pray for someone's healing as long as they refrain themselves from saying Jewish phrases in reference to themselves such as "asher kidshanu...etc", unless there is some bnei Noach prayer I don't know about that Noach was commanded to pray.
Just remember that all non-Jews don't follow the Sheva Mitzvot and could be in Avodah Zarah and then would such a blessing matter? It might even be harmful?