Bruce, you're quite right about it being illegal to deface Danish coins in Denmark, hence the use of Norwegian and Swedish ones.
As to this specific "advertising token", there may be more to it than meets the eye. There are various known Danish hotels and other businesses that used overstamped foreign coins for advertising, many of which can be traced through their owners' entries in directories to specific addresses. One prolific one is Allan Dahl.
Doing a bit of googling in Danish yielded
this discussion on Samlerforum about just this token. (Be aware if you use Google Translate that posts 1 and 3 are in Norwegian and 2 and 4 are in Danish

) Unfortunately neither of the links given by vestmar on that page are live any more.
The same is unfortunately true of the late Jørgen Sømod, who was *the* expert on Danish tokens. I therefore credit his opinions and findings considerably more highly than the average random comment on the internet. His theory is:
Det er en dansk polet beregnet til at aktivere automatdøre til lokummer eller closetter, som detr rettelig hed. Ordet closet var dog i manges øjne for vulgært, hvorfor det blev omskrevet til corset.
Denne polet har i bogen Poletter & Pengetegn bind 2 nr. 4706, hvor jeg har registreret årstallene 1875, 1876, 1878, 1896, 1899.
This is a Danish token supposed to have been used to activate automatic doors to toilets or closets, as they were properly known. But the word closet was too vulgar in many people's eyes, and it was bowdlerized into corset. This token is no. 4706 in vol. 2 of Poletter og Pengetegn [Sømod's series of books on Danish tokens], where I have recorded the following dates: 1875, 1876, 1878, 1896, 1899.Actually it's probably worth translating the rest of his information (post 4) properly as it is relevant and interesting:
De dukker op omkring 1901. Senere end 1899 og før 1902. Der kendes ingen overstemplinger i disse serier med årstal senere end 1905. I mange år troede man i samlerkredse, at det var reklamemønter i stil med visse udenlandske. Men, CORSETHUSET og CLOSETHUSET stod ikke i telefonbog eller vejviser. Andre var så små forretninger, at de ikke var kendt af alle og dertil, at adressen ikke var angivet på mønten. Jeg søgte da en fællesnævner for alle disse 5-ører og først da jeg blev klar over, at CLOSETHUSET ikke var et firma, men et lokum, gik det hele op for mig. Et af indslagene refererer til en cykelhandler her i nærheden af, hvor jeg bor og cykelhandleren eksisterede vist stadigvæk. Dagen efter, at jeg havde udtænkt brugen henvendte jeg mig til cykelhandleren, som på daværende tidspunkt havde haft forretningen i mere end 50 år og spurgte, om man i tidernes morgen havde beskæftiget sig med andet end cykler. Han fortalte nu, at dengang han overtog forretningen var der en dame, som fortalte ham, at hun havde samlet låse for hans forgænger. Det har selvfølgelig været sådanne automatlåse og cykelhandleren har reklameret for sig selv. Mønterne blev fortrinsvis brugt på trarverlige småhoteller og udskænkningssteder.
They turn up around 1901 - later than 1899 and before 1902. No overstamped dates later than 1905 are known. For many years it was believed among collectors that these were advertising jetons in the same style as certain foreign ones. But CORSETHUSET and CLOSETHUSET were not to be found in any telephone book or directory. Others were such small businesses that they were not generally known and moreover no address was given on the coins. I therefore looked for a common denominator for all of these 5 øre coins and only when I established that CLOSETHUSET was not a company but a toilet did the penny drop. One of the directory advertisements referred to a cycle dealer near where I live, which was probably still in existence. The day after I'd worked out the purpose of the token, I went to the dealer, who at that time had had the business for more than 50 years, and asked whether back in the day he had occupied himself with other things than cycles. He told me that when he took over the business, there was a lady who told him that she had put together locks for his predecessor. The locks were of course these automatic locks, and the cycle dealer had been advertising his business. The tokens were mainly used in small hotels and bars. This doesn't quite hang together, as as far as I can see the cycle dealer has not put his business name on the tokens. But it might have been known in the area that he was also responsible for the toilet locks and that "Corsethuset" became associated with his business.
I'd be interested to know what if any reference or background Greg Brunk has for associating the business Corset-Huset with Østergade 29, as Sømod doesn't mention this.