1/ Unlikely that the EU would ever agree that the EAW would *fully* apply to a non-EU country, since it would require some Member States to change their constitutions to allow their citizens to be extradited outside the EU.
2/ However, the EU might agree to a treaty on fast track extradition with a non-EU country, which contains most (though not all) of the features of the EAW. The precedent for that is the EU/Norway/Iceland extradition treaty, which has just entered into force.
3/ The political declaration already commits to negotiate a future treaty on fast track extradition with the UK along these lines. While the EU position is no negotiations on the future relationship before Brexit Day, the declaration might conceivably be fleshed out. 
4/ As for the CJEU, the frequent claim that the EU will demand CJEU jurisdiction in treaties with non-EU States contradicts EU practice in this field. Here's the text of the EU/Norway/Iceland extradition treaty on this. No requirement for CJEU jurisdiction, just case law review.
