In your case, I agree W-2C is the way to go, especially since NY wages are incorrect to start with.

In other case, IL will only allow a credit to be claimed with respect to non-IL income based on its own sourcing rules under IITA and using IL income as the base.  This would be a problem if the other state taxes income that is exempt from IL or has a different sourcing rule (e.g. NY taxation of employees who telecommute not for the convenience of the NY employer) where non-IL source income may then need to be adjusted on Sch CR based on IL sourcing rules.  So long as these adjustments are made, the credit should be allowed whether filed electronically or on paper.