You aren't going to be able to write any .NET windows application without the .NET framework installed on the client machine.
So your options would be to change to a language that does not compile to an intermediate language. Perhaps C++ or C or something of that sort.
Of course most, if not all, windows machines already have some form of the .NET Framework installed on them by default. So you might not have to install anything extra if it is already on the machines you are deploying too. If the framework is already there then you can do a copy and paste deployment if you really want to. Just run the exe and it will work.
I think the thing you really need to do here is find out exactly why they don't want frameworks installed with the application. Then see if you can work around or resolve the problem.
A web app is still probably the best option for this type of requirement though.