I just want to make sure I understand what you are saying. You are going to go from LGA to YYZ on one ticket. Then you are going to take a flight from YYZ>DTW>SHA. These are separate reservations. All of them are 006 tickets? January weather in YYZ and DTW are a factor to consider. Checked bags? Customs in YYZ?

That all said, delta could be accommodating. If you are willing to take the risk and not get to SHA and could be flexible if they need to reroute you a day or two later and you can stay in DTW.
They may charge a fee based on why you are delayed.
They may take pity on you. Maybe not.

I can't tell from your profile if you have status with delta. If you don't...that is also a factor.
So, are you a risk taker?