I am not sure with all the percentage registries...but with the ones I am familiar with I think both sire and dam have to be registered...even if they themselves are registered as percentages...most associations these days want to be able to track EPD's and know for sure what they are putting papers on and they really cant do that with animals that are out of non-registered cattle.
And I think you will probably have to show her as a cross at the Badger...I dont know how they do it up there, but around here for the steers its all based on classification, so animals dont have to have papers, they just have to meet the breed standards. But you have to be careful at the majors...if say for example you had a main cross that had alittle extra leather but was stout so you tried to classify him american so he would compete better and got to the show and the classifier said he didnt have enough ear...then at most shows they would either disqualify you or kick you to the exotics...so if your classifying one you better be sure he meets enough breed characteristic to actually classify.