To get this to work, you'd need to prompt the client to download the file from the server to the local machine. The latter would, of course, need to have the Java runtime installed in order to run the .class file.
The code to prompt the client to download the file would be something like this:
string fileName = "Hello.class";
string filePath = "C:/Hello.class"; // or wherever it's saved on the server
Response.ClearContent();
Response.ClearHeaders();
Response.ContentType = "application/java";
Response.AppendHeader("Content-Disposition", "attachment; filename=" + fileName + ";");
Response.TransmitFile(filePath);
Response.End();