You would be filing an amendment, not an extension. If you are amending a return and expecting a refund from the IRS, it is usually best to wait for the refund before filing an amended return. You can certainly wait to mail your amended return after your check has been cashed if you prefer.
The instructions would not have required you to send a W-2 with the payment, only the voucher that printed with your return. Electronically filed returns do not require W-2s to be mailed.
You can send a copy of the W-2 with your amended return, but it will not be required then either. The IRS will have the electronic version from your employer.
