Check out this thread -
https://bitcointalk.org/index.php?topic=717790.0It contains a list of casinos with info on whether they request for kyc or not, you can also read their terms for the exact amount that triggers the requirement to submit documents.
You won't have trouble with kyc on most casinos here on the forum if you're withdrawing below $2,000 to $3,000, but always do your research before depositing and bear in mind that casinos always reserve the rights to request for kyc at any time.
The link you provided can help the Op to know the casinos that doing KYC and the ones that are not doing KYC. And as you said, if the Op is withdrawing small amount, I think there will be no KYC requirement but when he is withdrawing big amount. And if he is withdrawing big amount then the no KYC casino he is looking for will also require KYC at that time so there is no KYC free casino in the industry for now. Someone made mentioned of DGbet and livecasinos, I don't think they will not ask for KYC when a gambler want to withdraw $10,000 and above. Op just prepare your KYC keep and register to any casino here that is reputable.