The OP stated that they have a koyorad and without knowing but assuming that its one of the nicer direct replacement ones than yes, STR would still stand as a class that this car could run in according to section L. in the Street Touring section of the rule book.
L. Engine cooling radiators may be replaced with alternate parts subject to
the following restrictions:
1. Radiator core dimensions (width, height, thickness) cannot be smaller than the standard part.
2. Radiator must mount to OE radiator mounts.
3. Fluid capacity and dry weight of the radiator must be no less than
that of the standard part. Installation of an alternate radiator may
serve no other purpose (e.g., to allow a cold air intake passage).
However yes, extreme attention to detail would be most suited if there are plans to go outside of "local" competition, but it's still good practice to at least be in the ball park, unlike some of the stuff we've seen in the past i.e. GS with a tune, GS with suspension, GS with a big turbo etc....