Tutein & Koch is another shop that I visited several times. It's an art supply store located at Farvergade 8, basically the same street as Grønlykke (Læderstræde turns into Farvergade as you walk toward city hall).
Their selection of colourful tags and butcher's twine caught my eye. Both are products of Denmark. I bought a few tags and a small reel of black & white twine.
Copenhagen was awash in washi tape. I bought two rolls at Hay House and then bought three more at Tutein & Koch. Washi tape, tags, and twine took little room in my small suitcase.