2 cents from a wannabe. :rofl:
It doesn't make any sense to me to cool from the outside. Only a fraction of the latent heat release can actually interface the CAC this way...the rest passes right around it.
If it were me, I would do chilling internally, using a WM spray, or nitrous, or even "liquid air".
The point is, if you want the heat exchange area that you are planning to use for power, to be cold, that is on the inside of the heat exchanger, not the outside. It makes sense to do it on the inside. Nitrous is so effective, partly for this effect.
In addition, you will cool more components that just the CAC, and they all get hot. I have never tried it, but I don't think you can do any harm spraying nitrous at idle. It's just oxidizer. But somebody correct me if I am wrong.