Well, Safer Soap would certainly not hurt.
I would not claim to know about the other two stronger "recommended" pesticides Malathion and Orthene.
I have used X-Clude 1600(Pyrethrins) myself to kill lots of bugs on my orchids and although I have sprayed it on the crown of my Phals, I follow up with some distilled water wiping and drying it afterward and have not had a problem. X-Clude 1600 will damage your buds/blooms. It specifically lists that it will kill mealy bugs on the bottle.
Neem Oil will kill mealy bugs as well and is always my preferred insecticide, but also is not the classic recommended for this "bug". I have many times sprayed Neem Oil on the Phal crowns followed by drying them without any problems at all. Neem Oil has not hurt my buds/blooms as I can tell when I've sprayed it.
Had a few mealy bugs a month or so back on a new catt plant I brought in and was repotting...bugs were a bit deep in the pot, about 3-4 of them. I sprayed the X-Clude all over the root ball and leaves and let it sit in the sink a bit. Then I repotted and watered it normally. Misted all the plants with Neem Oil every 4 days or so for about 2 months.
If you use X-Clude 1600, wear gloves b/c it can leak on your hands. My fingers would get a little numb when this happened so I wear gloves now.
I kill bugs. I am at war with them. I am the Clint Eastwood of bug-killing. There is nothing too toxic for me to try. If that stuff didn't work, I would not have rested until they were all yep, dead.