I did CR1 so can’t speak first hand for k1, but my understanding is they check the sponsor (you don’t need to provide any evidence etc) but provided it’s not a serious crime as mentioned, there’s no issue
these are the crimes covered by the act that would potentially bar you:
Crimes Covered by the Adam Walsh Act
The Adam Walsh Act applies to crimes committed against children, generally defined as victims under 18. Most of these offenses have a violent or sexual nature. They include solicitation, solicitation for prostitution, child pornography, voyeurism, internet sex crimes involving a minor, kidnapping, and false imprisonment, among others. Kidnapping and false imprisonment are not included if a parent committed the crime. The Adam Walsh Act also covers any convictions in foreign countries of equivalent crimes, unless the legal system in the foreign country did not give the defendant a fair trial.
You should have no issue