You can definitely mount the heatsinks to the exterior. Here's how I did mine:
I cut a large rectangle out of the box, then another rectangle from a sheet of aluminum that was about 2 cm larger than the cutout. Spread a bit of thermal compound on the mounting side of the SSR and heatsink, then bolt the SSR to the heatsink through the aluminum plate. Bolt the plate to the box, and seal it with some silicon if you feel the need.
As far as noise from the SSRs, I have my CP packed really tight, with no shielding on the RTD wires and haven't had any discernable issues so far. Other guys have shielded their RTD wires.