Is there an iOS4 app that when clicked will perform the same function as Settings->Airplaine Mode on/off?
Not without a jailbreak.  If you get a jailbreak there are various ways to do things such as switch airplane mode on/off, adjust screen brightness, turn wifi/3G on or off.  The app SBSettings is one such example.  You'd be better off diagnosing your AP problem than jailbreaking your phone for just this feature though in my opinion.