Component change following design freeze
If your product is for sale in the US, check out the regulations/policy around Permissive Changes.  FCC Publication 178919 talks about permissive changes and the requirements for testing and filing if required.   The link below should work, but if it doesn't just search the FCC OET Knowledge base for that publication number.

https://apps.fcc.gov/oetcf/kdb/forms/FTSSearchResultPage.cfm?switch=P&amp;id=33013

If your product is for sale outside of the US, then CE regulations/EU directives are most likely applicable.  Depending on what the product is and what EU directive it falls under, contacting a test lab/Notified Body would be your best bet. 

In either case, it would be worthwhile to consult with the test house who conducted your original certification testing.  You may not need to re-test everything (or anything) depending on the nature of the changes.  Since you-are-not-a-lawyer and i-am-not-a-lawyer, we engineers get to rely on third parties to give us good advice on these matters.

(If you don't trust your test house to give you a straight answer then you need to find a new test house!)