I up-voted your question because I have a very similar issue (only I want to open Acrobat Reader full, instead of the plug-in, from a normal webpage and not an Air app). However, after researching (Googling) it a ton, I've become convinced that there is no way (for either of us).
The problem is that the browser essentially just does a simple MIME-type lookup to determine "I should open this in the Reader plug-in". As a result, there doesn't seem to be anything a given web page/air app can do to make the browser use a different app; the only way to change things is for the user to edit their browser preferences. The only thing that might work is if you changed the MIME type of the file being served ... but then that would just prompt the user to pick a program; it wouldn't automatically open in the standalone reader.
Anyhow, I'd love to see someone else post an answer proving me wrong, but after spending several hours on this I'm afraid we're both probably out of luck.