I don't think it can be done. Even if you copy all the registry settings and files and manage to register it all in a new machine in a small time, you still risk having something which won't work properly, and the cost of keeping this "custom installer" updated would be big.
The best way to get that result is not using .NET (or any similar framework), so you can build a standalone executable and have it up and running in seconds. However, since I guess your app is already developed and it would be too expensive to re-build it from scratch, the other options might be using a virtual machine. You can set up a virtual machine with the operating system, .NET and your app installed and configured.
But still you would have to install vmware - unless you demand it to be installed on all machines before you setup your app. But in this case, you can simply demand that .NET is installed prior to using your app, it shouldn't be too much of a problem. I think this is the best way to solve your problem without dropping .NET. Good luck.