It seems I have underestimated the Danish oil reserves. However, oil export is a small fraction of its economy. I haven't been able to find an accurate figure, but according to Danmark statistik [1], it was about 8.17% of Danish exports in April 2014, which is very far from making Denmark into an oil-based economy like Norway is.

1: http://www.dst.dk/pukora/epub/Nyt/2014/NR300.pdf (in Danish, but it would go under the "Brændsels -og smørestoffer o.l." category)