However according to the Danish Working Environment Authority's Executive Order no. 589 § 60, it is the employer's duty to ensure that there is access to clean drinking water, during work and not just during the break. And, according to an ancient arbitration from June 19, 1959, the workers are also entitled to take small breaks where you can take refreshments.
It is up to you to negotiate the specific circumstances in place with your employer, but you have the right to quench your thirst while you are at work.
If you have not been able to agree with the employer, please contact your union.