gee....someone finally asked a question that I feel somewhat qualified to answer, primarily on the basis that I was doing the same job up till about a month ago. I'll go ahead and give you my most blunt answer...
In all candor, what that checkover is, is a buncha fuzzy political feel good BS. my post orders pretty much confirm that with statements such as "there is a very special emphasis on public relations at this post" and "we are looking for very big bombs that are at least five hundred pounds" So now the secret is out. You can carry your bombs to the airport all you want, as long as they don't exceed 498 pounds....
on a more serious note, we weren't looking for knives, axes, machettes, firearms, alcohol or anything else, we were giving a very quick cursory inspection for explosives and that was it. I never gave anyone a hard time about what they had in there car or truck, as long as it didn't resemble a bomb. Not to say that I wouldn't have if something seemed amiss, but that just never happened.
Obviously results could vary according to state, airport, security agency, and the officer themselves, but as a whole, no one is likely to give a crap what kinda edged tools you have in your vehicle, as long as you aren't covered in blood and and speaking in tongues as your eyes roll around or something.
Hope y'alls day is a good one!