My everyday 25 year old Buck-Lite with a good quality Stainless steel blade is all that I use for airlayering. I airlayer a lot of tropicals. The $8.00 knife is probably good enough to get the job done, is it a stainless or carbon steel? I use the rounded front portion of the blade to scrape the membrane off trunks off once I have removed the bark (especially on BRTs whose trunks have started to flatten and flute), using a hawks bill would be difficult for me. For grafting I use a Due Boui Italian high carbon steel knife sharpened on a 5/ 25 micron diamond stone with oil, it will get surgical sharp. I never sharpen a knife on a grinding wheel or a machinist file. ( Or the sidewalk like we did when we went fishing as kids!) Old knob and tube electrical porcelain insulators work good for a quick polishing. I'm getting ready to do a hundred or so airlayers on a hedge of Divi-divis and Xylosma bahamensis- Spring is here!
Ignorance can be a Powerful Tool, when applied at the Right Time, it can Surpass Knowledge!