Yeah, you could maybe still create all the CIECAM02 values related to your input (within some granularity limit) and discard those producing values outside the CMYK gamut.

Or you can try "gamut mapping", on them: this is through algorithms to get the closest "narrow gamut color" in CMYK from a color in a "wider gamut color space" like CIECAM02.

Search for "gamut mapping algorithms" or "gamut compression".