It has taken 2 pages of posts to get simple & accurate information which changes the entire picture. It would be a good thing if OP checked his tickets for the operating carriers and times because none of this will matter if he doesn't get them straight.

It doesn't matter what the "DL lady" told OP on the phone because OP is on a WS-operated flight and if WS causes a delay into YYZ, it is WS which is responsible for OP's onward travel if there is any on his ticket. But, his ticket terminates at YYZ so far as WS is concerned. Thus, WS will politely smile at OP and tell him that it has met its obligations. End of story.

OP then appears to be booked onward on a DL-operated flight which he will have noshowed for. At that point, the DL ticket will have been cancelled. This will include all onward segments. Will DL reinstate it? Perhaps. It will take time and it will take effort and because there are other onward carriers involved, it is not as simple as DL waving a wand (and waiving fees pardon the pun).

Thus, the key is to allow oodles of time to allow for IRROPS, border issues and anything else that can go wrong. A cheap airport hotel would make sense, lower stress and serve as a smart insurance policy.