That would be fine to file a second 4868 including your wife's name. As she does not have an SSN now, the 4868 will need to be mailed. You can fill it out manually. In the box for her SSN, you can write in "W-7 to be applied for."
Simply refer to IRS Form 4868: Application for Automatic Extension of Time to File U.S. Individual Income Tax Return, complete and print the form, and send it to the IRS address for your state.
