There are a couple of ways to sign without a normal danish NemID depending if the signer is from one of the Nordic countries or the rest of the world.
Denmark, Sweden and Norway
It is possible to sig with NemID in Denmark. In Norway and Sweden you can sign with BankID.
Rest of the world, and people without E-ID
There are a couple of options here. If the signer is a employee of your company they can sign with a employee NemID. This is something your own company can get for all employees. You can read more about and order employee NemID here https://medarbejdersignatur.dk/ (Site is in danish).
The last option our touch functionality. When creating a casefile you can select the option for the signer to sign with touch. You can read more about touch signature here.