You can simply select all text, in Word or InDesign, and click the Black color swatch. That will reset or override all styles to black.
If you want to avoid spot overrides, make sure all styles are already set to Black. (Ideally, all the Word styles in use should be so configured, as well as the InDesign styles; you may have to clean this up at the Word stage on any received document.)
There are also methods to force-reapply styles throughout a document and remove any existing overrides to varying colors (even "other blacks.")
The blue of hyperlinks, in Word at least, is a live override, not a truly applied color. You can preserve the hyperlinks as a character style in ID and do pretty much anything you want with them in styling.
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