What does "if you offer Wikipedia content to them to modify" mean? Do you mean *modify easily* as in providing an edit button say for that Wikipedia content?
Even if I don't import any wikipedia content at all, some users may still (manually) copy and modify wikipedia content (or content from any other source). Presumably this would fall under fair use anyway?
If the content on your site is modified Wikipedia content, then it must be licensed under GDFL, regardless of how it got there. It's possible that small amounts of Wikipedia content would qualify as fair use, but significant parts of articles almost certainly wouldn't. It all depends on exactly what you are doing with it.
As long as you keep Wikipedia and modified Wikipedia content clearly separated from other content, there is no problem having the other content under a different license.