To determine which application is associated with a specific file name extension you can look in the registry under HKEY_CLASSES_ROOT.
Easier is to use the Windows API function FindExecutable() - see the following example.
The code shows the fully qualified associated application or the last error (using GetLastError).
program Project1;
uses
Forms, Dialogs, ShellAPI, SysUtils, Windows;
{$R *.RES}
var
sApp : array [0..256] of char;
begin
// this should return something like c:\program files\office\excel.exe
if FindExecutable('c:\temp\xxx.xls', nil, sApp) >= 32 then
ShowMessage(sApp)
else
ShowMessage(SysErrorMessage(GetLastError));
end.