Every time I've flown ex-JFk on CX, they always detach my boarding pass. They've always given back the full BP ex-YVR and ex-HKG.

Would it be possible to print out the BP from OLCI and then go to the counter to ask for the BP to be printed on CX stock but when I go to the lounge and board the plane, just use the OLCI paper version?

In that case, will they take the paper away but if they do, what should I put in my coat when they hang it in the closet since they always ask me to put my BP in it.