Overriding default search URLs

Is it possible to override/modify default Yext search URLs to a different format?
I just wanted to know if it’s possible to do it, so users who used our previous search engine can still use their bookmarked pre-faceted search pages when we switch current search engine to Yext. I believe this can be tricky, so I am looking for any hints/opinions on that.

Our Yext search URLs with two active facet filters looks more or less like this:
https://example.com/search?query=test&referrerPageUrl=&facetFilters={"c_parentTerm"%3A[{"c_parentTerm"%3A{"%24eq"%3A"Test"}}]%2C"c_productVersion"%3A[{"c_productVersion"%3A{"%24eq"%3A"2.0"}}]}&filters={}

while original one w/o Yext looks like this:
https://example.com/search?f[0]=product_area%3APrdVer88