I moved from Switzerland to Copenhagen in 2005 but there is not much wet shaving related to find in the city. IMO.
Some new barber shops are popping up here and there in the last 2 years, mostly with arabic background.
There is a cosmetic chain called Matas, you find these everywhere on highstreet locations. They have a farly OK unscented shaving soap and 1 or 2 beginner brushes in their range. As far as I know, thats it.
Little add on:
On the Tax Free shop at CPH Airport, the new Acqua di Parma Barbiere Shaving Soap and Aftershave Lotion are available beside other ADP products. You find these also downtown at the 2 most popular / exclusive department stores Magasin and Illums but the products should be less expensive at the Airport.
If you go to the part of Copenhagen called Frederiksberg and find Frederiksbergcentret there is a shop-in-shop called Mens Corner in the Matas shop. They have plenty of stuff from several well known makers.