Yes, you can register in Unioo without a CVR number, whether or not your association is linked to a financial institution. Simply leave the "CVR number" field blank.
Most associations do have a CVR number, so it's worth checking again to see if yours exists. It may just need to be activated in the Danish Business Authority’s CVR register on virk.dk. Read more about this here.
Having a CVR number also comes with advantages—it makes it easier for financial institutions and partners to identify your association and access relevant information.