You'll only need to complete the lowest level of KYC where you'll fill in the basic information (Name, address, etc.).
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I would probably prepare to give way more info, even if in registration phase they wouldn't need as much.
As at some point, depending how seriously you are playing, (or if you are unfortunate enough to have suspicious transaction history etc), you eventually need to give more information with the KYC.

And this could also happen to older accounts that didn't need it in the past as well. Shuffle has been pretty clear that they have prepared for the growth and future of regulations, so while they are doing absolute minimum now, that minimum kyc could change even later this year.