You can try writing a DLL for this in another language (for example C) and then using the proper 'Call Library Function' VI to call it. You can find it in the Functions palette under 'advanced'.
However, as you already guess, LabVIEW was not made for these things, so you might want to jump to something like C or assembler entirely.
It's also possible that Int 13 calls are restricted under various versions of Windows (especially NT/2000), so even with the mentioned DLL or assembler you might not have enough luck.