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"
The difference in nuance you describe between "We do not have workers here" and "We have no workers here" doesn't exist in English. Although they are grammatically different, they are identical in meaning. On the other hand, the two ice-cream sentences you quote are substantially different.
While I agree with you, the translators do not seem to accept (especially in simple constructions) some translations that might seem perfectly acceptable to English speakers. In this case, "ikke" is not considered precisely the same as "no." You have to use their preferred model. They do seem to be more flexible at higher levels, which often require creative translations for complex sentences.