You need to spend a LOT more time learning about the modding scene before you go any further.
1. If there was a way to run a homebrew WITHOUT hacking the Xbox (via modchip or exploit), why would there be modchips or exploits? That part of your 'request' is rather pointless. You WILL need to either use an exploit (read about it in the exploit forums) or a modchip.
2. Your vague description is uneccessarily vague. To be able to port an app to the Xbox, it must:
1) have COMPLETE source code in C++ and/or original assembler (not that disassembler crap). Not managed C++, C#, or VisualBASIC.
2) NOT use any GDI APIs, or use the UI features of Windows
3) If it's a game, it should be written to use DirectX, not OpenGL.
4) Not require any special drivers, unless these can somehow be ported over as well - not terribly likely in the case of USB drivers, for example.
5) Did I mention COMPLETE source code? Disassemblies are worthless. Games without their 3-D engine (as many FPS games have their "game" code released, but not the most important bits - the 3-D Engine that drives them) are worthless.
Try being far less vague. Does the app involve hardware? If so, is it tied to the USB port, or does it require hacking to install? Is the app a strictly DirectX affair, or a GUI app?