The main risk in replacing a website is throwing away accumulated search visibility along with the old design. It is avoidable, and it is mostly about discipline rather than budget.
Keep existing URLs wherever they still make sense. Where they must change, map redirects one to one rather than sending everything to the home page. Carry across page content and metadata that was already earning attention instead of rewriting for the sake of it.
Build on a staging copy, check the important pages before launch, and watch search performance and error reports for a few weeks afterwards so that anything missed can be corrected quickly.
If a rebuild turns out to be the sensible route, the review notes what should be carried over — URLs, redirects, content, metadata and analytics continuity — so the decision is not a leap in the dark.