Hi Camille

I soak the pot/roots in water first so the roots are 'full'. I find using the neem oil and soap mix doesn't seem to cause any problems - no oily residue at all. And nice clean shiny leaves as a bonus.
I use 10ml hort soap + 5ml Neem oil to 1L lukewarm water and put it in a pressure sprayer. And fill the cache pot.

Warning: the only orchids I've used it on are Phals. No experience on other varieties.