We have no workers here is perfectly good English.Sometimes the translation can be exclusively American.
But it does not have the same meaning as the danish sentence.
"Vi har ikke arbejdere her" = "We do not have workers here" -> We never have workers here, as we never hire workers.
"We have no workers her" = "Vi har ingen arbejdere her" -> At this time there are zero workers here, but we might hire some later.
Difference is the same as "You never use flour in ice cream" vs "There is no flour in this ice cream"