Rather than being described as core emotions, surprise and disgust tend to be viewed as emotional motivators. They may surface in combination with any core emotion. They can increase the strength of any core emotion or a reaction/action/behavior related to the emotion.
Surprise can strengthen a core emotions with a sense that whatever happened was completely unexpected. Regardless of whether it was good or bad, happy or sad, or indifferent, you were not expecting what happened.
Disgust can strengthen a core emotion with a sense of revulsion, aversion, repugnance, or profound disapproval aroused by something you perceived to be extremely unpleasant or offensive or a breach of good manners; or something you hate or abhor, or consider to be an abomination.