How we do it in Australia land. See attached.
I query the cold water bath: mechanical to retain coolness? How consistence cold is the batch? Should this be the CCP and checked and not the product? Are you able to purchase a blast chiller? You already know what the critical limits are for your cooling... you have to ensure the process and the equipment being used is capable of this. This is where I would place the CCP.
I see no problem of testing outside of product if soup is thinner consistency, but it may depend on size of product? Would the outside temperature be consistent with internal? If large packaging, and thick soup consistency then probably not?
Also, is product fully sealed and packaged prior to placing into cold water bath? If so, shouldn't product be aired out first, to allow for a quicker cooling timeframe?
If product is opened, then assurance required that staff would diligently used a cleaned and sanitised thermometer for testing.
If overall, you are confident with your processes, then perhaps consider a monthly or bi-annual, or annual validation only of product, but a daily validation of the equipment used to cool product down.