Single click? Nah.
I believe you can select multiple MS-Office documents (though I'm not sure about multiple office document types) in windows explorer, and then select Print from the context (right-click) menu. If the type of documents are more than just office, it becomes more difficult, essentially you do have to open and print each file, but the process can be automated.
You need to know which program the file is created with, and have access to it. You need to know the command that program uses to print its files and be able to run those commands from the commandline, usually through switches, perhaps through its API, or possibly macros that can be run externally, or a combination.
With all that info, you can create a script that iterates through a directory listing and switches, depending on which file type it is, to access the correct program's printing functions through the API and prints it (opening and closing the program if necessary), before moving onto the next file.
Your first step is probably to google 'command line switches' for each application that has a file that you want to print.
A couple useful links/tips:
Print from Word command line:
WINWORD.EXE test.rtf /q /n /mFilePrintDefault /mFileExit
/q - no splash screen; /n - don't open default doc
Printing adobe pdf from command line: AcroRd32.exe /t <filename.pdf>
/t <filename> <printername> <drivername> <portname> - Print the file to the specified printer
The above examples assume windows. It's the same process in *nix (and I assume OSX/mac), but obviously the programs owning the files and the commands to run them will be different.
After writing the script, setting it up as a shortcut or otherwise making it executable (lol, and testing), you could double click to get what you're looking for.