The law is indeed very vague. The only parts of relevance are the following:
Source - 941.23(2)Any person, other than one of the following, who carries a concealed and dangerous weapon is guilty of a Class A misdemeanor
The exceptions are if you are or were a cop, if you are in your own home or place of business, or if you have a concealed weapon license.
In the cast of the latter two exceptions, the weapon must be one of the following:
Source: 175.60(1)(j)"Weapon" means a handgun, an electric weapon, as defined in s. 941.295 (1c) (a), a knife other than a switchblade knife under s. 941.24, or a billy club.
Putting it all together in plain English:
If you are not a cop, not on your own land, don't have a concealed weapon permit and you are carrying any kind of non-automatic knife concealed, it is a judgement call that must be made by that police officer, and if arrested, another judgement call that must be made by the judge and jury. Case law indicates it is the totality of the circumstances where the knife is found, what the apparent or expressed intent of the knife carry was, and the design of the knife being primarily intended as a weapon.
A notable case illustrating the capricious nature of the state's knife law is State v Ronnie Malloy, 2005. Malloy was a pugnacious drunkard who got in a fist fight at a gas station. The police were called and arrested him for disorderly conduct, during which they found he had a 4" folding knife in a belt-sheath. The knife's description sounds rather unremarkable, and it was likely something similar to a Buck 110 Hunter. Malloy claimed the knife was for work cutting boxes and for fishing. In spite of this non-combat purpose, the jury chose to ignore his statement as "self-serving" and convicted him of carrying a concealed dangerous weapon based on no other reason than knife having "a very sharp, pointed blade approximately four inches in length." This conviction was upheld on appeal.
Frankly, such a ruling on a law like that would scare the crap out of me. The statute is clearly unconstitutionally vague, but WI seems to be following the tradition of NY and some other states ruling "It is not unconstitutionally vague nor does it violate the Second Amendment cuz...uh...cuz I'm an appeals court judge and I say so! Nyan-nyaaah!"
So if you want to comply with the law, you can either carry something that is blatantly tool-like, such as a multi-tool pliers or a SAK, you can make sure that anything you carry is openly visible at all times, or you can get one of those new concealed weapon permits (which unlike most states, covers knives, tasers and batons) they just started issuing due to that new law this year.