I dont know the answer to your question but first:
I'd check what ratios the Stilo has against the sporting, It may have taller less sporty ratios which you may or may not want.
Even if same box the gear lever linkage and other bits may differ.
I'd go down the scrappy with a digital camera and take some pics of the box and compare with your gear box. Its easy to miss something from memory.
Even if its same box you may need to swap some bits with your old box.
Are you able to attempt job your self or do you have a mechanic who's a good mate, if not and you would be taking the box to a garage to do the work for you then your just asking for a huge bill and are best to forget the idea.