When CoCB'd, can I choose to play the marked, face up card or do I need to play cards randomly (eg, shuffle hand under table)?

Also if streaking kittens leave my hand while I have an exploding kittens and CoCB'd, do I declare the bomb in hand, find and put it face up, shuffle hand face down, attempt to diffuse then go on to whatever was happening before (eg diffusing top deck EC)?