How transfer only one app from my old 3GS to my new 4S

I've already sync'd my old 3GS iPhone with iTunes and then sync'd my new iPhone 4S with iTunes, so all my old stuff transferred to my new iPhone.  Now I want the old version of a certain app (Sleep Cycle) that's on my old phone.  I do not like the new version of Sleep Cycle. 

Is it possible to just transfer that app from old phone to new phone?

I tried plugging my old phone into my computer (Dell desktop), chose do not automatically sync, went to devices, apps, and unchecked all apps except Sleep  Cycle.  When I then clicked "apply," I got a warning that all my apps except Sleep Cycle were going to be deleted.  I don't want to delete them.

Any help is greatly appreciated.