There is evidence in Koran that Sharia law is meant to be used only for Muslims. To even suggest using any part of Sharia law to non-Muslims is to go against the intent of the Sharia itself as prescribed by Allah.
Read verse 48, from Surah 5:
“ And we have revealed to you the book in truth confirming that which predeeded it of the Scripture and as a criterion over it. So judge between them by what Allah has revealed and do not follow their inclinations away from what has come to you of the truth. To each of you, We prescribed a law and a method. Had Allah Willed, He Would have made you one nation but to test you in what He has given you; so race to good. To Allah your return all together, and He will inform you concerning that over which you used to differ.” Surah 5, verse 48
Another verse which illustrates that God is the only judge for non- Muslims
is Surah 45, verse 17. Actually we should read from verse 16 &17
" And we did certainly give the children of Israel the Scripture and judgment and prophethood, and we provided them with good things and preferred them over the worlds." verse 16
" And We gave them clear proofs of the matter. And they did not differ except after knowledge had come to them. Indeed your Lord will judge between them on the day of Resurrection concerning that over which they used to differ. "
Additionally to define Jihad as convert people to Islam is also a false notion. The duty of Muslims is to stay Muslims not to convert others to Islam.