The 1096 goes to the IRS, not the payee. You will need to file one. Some vendors that you can use to e-file a 1099 will issue the 1096 automatically, make sure you read the rules and instructions carefully.
Quick Employer Forms FAQ are here,
If you use the Online Quick Employer Forms the 1096 is automatically filed electronically. Ifyou use the Windows Home & Business program you have a choice. If you use the built in W2/1099 Reporter you have to mail in the 1096 & 1099 to the IRS yourself.