Not sure whether httrack has an option for it.

Could you do it with a search-and-replace tool after you get just the HTML
files?
I would try something like sed (Linux) or InfoRapid Search and Replace
(Windows) to replace links like <http://www.site.com/videos/catsbirthday.mpg>
with "videos/catsbirthday.mpg".

Do you have an example?