It depends on the organization. Some larger financial institutions are sometimes more likely - or even bound by internal policy - to simply trigger their standard card-cancellation procedures.

Instead, one could present the financial institution with the hypothetical question, and then only give the specifics if the institution's policies are non-destructive.

If the finder is a decent sort, and has the time to try alternatives, I'd rather get the cards back intact than to have to do the cancellation dance.