If a category at
http://dmoz.org doesn't have the "suggest URL" link, then it is not a category where sites should be suggested; you should look at its subcategories to see which one would be most appropriate.
There is no reason, ever, for any editor to "help complete a suggestion". If editors think a site is worthwhile, they can always simply add it to any category (if not directly to public view, at least to "editors' suggestions.) Look at it the other way around. The "suggest URL" link is for you to help the editor get sites into a category. All help is strictly voluntary -- you need feel no obligation, if you do not wish to help.
A caveat: you mention "sites". "A personal site" may well be worth looking at, but "a person's sites" nearly always are NOT. That is one of the reasons that the submittal policies (which you'd have seen if you'd clicked on an "Update URL" link) are so specific about NOT suggesting "related" sites. (Nearly always, all of "your" sites will be by definition related to each other because they are from the same entity.) So, you should basically pick one of your sites, make sure that the surfer can get from it to all your unique content, and suggest it only.