You Do Need power plug adapter while traveling from Denmark to South Africa.

Here is Why You Need An Adapter

The outlet and plug type used in South Africa are C, M and N and in Denmark are C, E, F and K. This is how they look like.

Denmark

In Denmark, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N