One millimeter slice in a tubed tire shouldn't be a worry, especially if you don't run at high pressures. Keep an eye on it. If it looks like it's getting worse, replace.
__________________
A race bike in any era is a highly personal choice that at its "best" balances the requirements of fit, weight, handling, durability and cost tempered by the willingness to toss it and oneself down the pavement at considerable speed. ~Bandera