"LOL"... Here's the Ill vendor list
https://www.dnr.illinois.gov/LPR/Pages/LicensePermitVendors.aspx
(The only time you need the Illnoise Registration is if you ride in Illnoise and your domicile is Illnoise)
Make sure you have a insurance card to because that is the one they are checking for in their so called safety checks as it draws the biggest fine...
Wi Snowmachine laws
Nonresidents — As a nonresident, you may operate your snowmobile in Wisconsin with your state’s current registration as long as the decal or proof of registration is prominently displayed and the snowmobile has not been in Wisconsin for more than 15 consecutive days. The proof of registration from your home state must be carried with you while riding and must be presented to an enforcement officer when requested. Once your out of state registered snowmobile has been in Wisconsin for longer than 15 consecutive days, it MUST be registered in Wisconsin.