The key is to modify your paid listings so hits from them can be identified. Once you do that, any traffic from search engines that isn't identifiable as paid is ... unpaid. That's all it is.
You make your paid listings identifiable by modifying the URL in the paid ads. Add parameters to the end of the URLs. The most versatile solution is to add three different parameters. WT.srch=1 will tell WebTrends it's a paid ad and will work with their preconfigured paid-search reports. But don't stop there. Add another parameter such as ppc=g (for "pay per click is google") for example. Then finally use a parameter to identify the keyword you are paying for, for example "kw=paid+term". This is a far better method than relying on the term in the referrer field, which may be surprisingly different from what you think you paid for.
You can use WT's canned reports but also be sure to set up a parameter analysis for "ppc x kw". Plus, use the ppc parameter as a profile filter to get a complete set of reports for the ppc traffic from just one of the PPC families. If you do this, take a look at the referrers report for that filtered profile. You'll get a list of all the affiliates and odd sites that have displayed your ads (those that people have clicked on). The SE Key Phrases report will also give you an idea of the variations of your paid terms that happened.
If you had WT's custom reporting in the higher levels of their product line, you could also do a very interesting report of paid keyword vs actual searched keyword, for each paid keyword. Some of the "matches" are pretty strange.
Finally, if your version is 7.0 or 7.1, be sure to upgrade to 7.5 which is the most stable.