I'm not a lawyer, but I play one on the internet.

Concerning search and seizure, it's not as much as a 4th Amendment issue as it is a statutory issue. Other states have explicit statutory language that allows wardens to inspect motor vehicles or boats while taking or transporting game. For example, MN Statute 97A.25 states,  "A person may not: (3) refuse to allow inspection of a motor vehicle, boat, or other conveyance used while taking or transporting wild animals."

These statutes have regularly been upheld as within the Constituional powers of the enforcement officers on the basis that, "the widespread knowledge of restrictions accompanying the privilege of fishing casts doubt on the reasonableness of an expectation of privacy that would allow an angler to refuse inspection of his catch"  and the state's mandate to manage and preserve the state's natural resources (see for example MN State Supreme court ruling in State v. Colosimo).

However, to the best of my knowledge, WI has no such statutory provision. To the contrary, the statute outlining the enforcement powers of the DNR states that officers must have reasonable suspicion, "WI 29.921(1) Generally. The department and its wardens may execute and serve warrants and processes issued under any law enumerated in the same manner as any constable may serve and execute the process; and may arrest, with or without a warrant, any person detected in the actual violation, or whom the officer has probable cause to believe is guilty of a violation of any of the laws cited in this subsection, whether the violation is punishable by criminal penalties or by forfeiture, and may take the person before any court in the county where the offense was committed and make a proper complaint. For the purpose of enforcing any of the laws cited in this subsection, any officer may stop and board any boat and stop any vehicle, if the officer reasonably suspects there is a violation of those sections" (emphasis added). The language in the new rules would allow for unimpeded inspection and, given the precedent established in other states, likely passes Constitutional muster.

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The NRB's VHS rules allow for exceptions to the "dead at the shoreline" rule with "with the prior written approval of the department, where the department has determined that the proposed activity will not allow Viral Hemorrhagic Septicemia virus to be transported to other waters." I'm sure that when live weigh-in permits are granted the 'prior written approval' will be incorporated into the permit.