C# Prevent copy of files to usb flash outside of our app

We want to add a feature that will prevent the user from adding files to a USB flash drive without using our application. The only thing I was able to come up with myself was to fill the remaining free space on a USB flash drive with an empty file. I could find no way of using the .NET API to do this that didn't take a long time as it had to create a file and write every single bit with zero's. From what I have read this may not be a realistic feature given the limitations of FAT but I wanted to post in case someone has had experience in this area. The solution needs to be able to work on slow flash memory and do so in about 30 seconds or less. The flash drives will be FAT16 formatted but would like your code to also work with FAT32. If these requirements are feasible then we'd like the code you provide to have a C# wrapper so I can just drop it into the code with little fuss. I want this be an all code solution so I don't want to have to call any external programs. For this project, experience and English proficiency are more important than lowest bid.