That's something of a trick question (not on your part, just in general).
While a true dagger is a doubled edged knife specially designed to stab with, jurisdictions that use the word "dagger" are not exactly consistent in their interpretation. The term "dirk" is used interchangeably even though a real dirk describes a specific Scottish dagger.
As such, the interpretations of these term vary both for officers (which is highly inconsistent) and courts. Sometimes a cop will make an arrest for a false edge or clip point, only to have it thrown out. So it's going to come down to where you are located.
In my experience, police aren't so interested in these petty technicalities of one thing vs another so much as what you're actually doing at the time and what you say (and perhaps their own biases). If you're some tatted up gangbanger being menacing around town and want some kind of weapon that the cops can't touch you for, you're probably SOL from the get go. Well-mannered hiker in the deep woods, perhaps not so much of a concern.
To the permit issue, we all wish there was a knife permit, but in the US there isn't such a thing in any state I know of. A few states extend their local CCW permits to knives, but many are strictly for handguns.
The legality of a LEO carrying any normally prohibited knife varies by state, but most have an exception in them for LEO that exempts them. Firefighters I actually have yet to see an exception for. Further, such emergency workers must abide by departmental policy beyond the law.
Hope this was helpful to you.
