Check with the vintage groups that you might be able to run with regarding tires. Most groups will not allow slicks and require DOT tires. SVRA has a list of allowed tires by race group.
http://www.svra.com/wp-content/uploa...ons_1215.2.pdf
I checked previously with SCCA and you can run a cobra replica in GT1, but they caution that it would probably not be competitive and it would not be vintage. You would be racing against modern vehicles.