What size tire on a 15x4 inch rim ?
A 165/80x15 is a one-size-up tire for a vw beetle.
None of my cars that use that size tire even dream about going fast around corners, but that's not what they're for.
Just make sure using a tire that small that you add some rear brake bias, assuming much bigger tires on the rear.
Edit: looks like 67 barracuda used a 215 on a 14x4.5 rim stock. So maybe a 205 or less (195?) could work on a four inch rim.