Well, the answer's actually fairly straight-forward.
Firstly, since Windows will open your media files by default with VLC, you can't rely on the 'usual' method involving ShellExecute, since that will also invoke VLC.
What you instead need to do is:
a) Locate the Windows Media Player executable
b) Locate the file you wish to play
c) construct a parameter-string to pass to WMP
d) call ShellExecute, with the full path to the wmplayer.exe file and the param-string from (c)
In practise, this code will play a file called "tada.wav", located in the same folder as your exe. (Tested on Win7 Home Premium)
void playFileWithWMP()
{
TCHAR progFileFolder[MAX_PATH];
TCHAR *desiredFile = "Windows Media Player/wmplayer.exe";
TCHAR mediaPlayerPath[MAX_PATH];
TCHAR *fileToPlay = "tada.wav";
TCHAR wmpParam[MAX_PATH];
TCHAR defaultFolder[MAX_PATH];
SHGetSpecialFolderPath(0, progFileFolder, CSIDL_PROGRAM_FILES, FALSE);
strcpy(mediaPlayerPath, progFileFolder);
strcat(mediaPlayerPath, "/");
strcat(mediaPlayerPath, desiredFile);
GetCurrentDirectory(MAX_PATH, defaultFolder);
sprintf(wmpParam, "/play %s/%s", defaultFolder, fileToPlay);
ShellExecute(NULL, NULL, mediaPlayerPath, wmpParam, NULL, SW_SHOW);
}