I had great success with Chemiclean. I just left my protein skimmer running and pulled the top off since I didn't have airstones. Also, I don't run carbon in my tank. I did feed during the treatment process bytheway. Sounds like you're going to be fine. Good luck!
I used chemiclean a couple months ago for a cyano problem, I didnt have any airstones either, so just let my skimmer run without the collection cup on. Had no issues at all and it got rid of all my cyano in a day surprisingly.