Where to marry in Denmark

You may try  Copenhagen or Frederiksberg, although it could take 3 to 4 weeks before you hear from Copenhagen Municipality about your marriage application, so maybe you could opt to have it at Frederiksberg.

Here's their contact info:

Copenhagen City Hall Wedding Office
Rådhusoplysningen
1599 Copenhagen V
Tel.: +45 3366 3366
Email: Bryllup@kff.kk.dk

Frederiksberg Town Hall Wedding Office
Stuen, værelse 16
2000 Frederiksberg
Tel.: +45 3821 2111
Email: vielser@frederiksberg.dk

Likewise you may check this website for how to get married in Copenhagen: http://international.kk.dk/marriedincph
The information about getting married in Frederiksberg is in Danish, but the general requirements to get married in Frederiksberg Town Hall are the same as what's listed in the Copenhagen website.

You may also check getting married at the following Kommunes:
http://www.haderslev.dk/sprogvalg/english/marriagehttp://marriage.sonderborgkommune.dk/procedure

Alternately, if you want to have someone arrange for your wedding in Denmark so you won't have to worry about it, you may check these websites:
http://www.getmarriedindenmark.com/http://www.lr-wedding.eu/en/home_en.html

Hope this helps 

The authorities need of course some time for the paperwork. About a fortnight is normal. That means that it may be difficult to find others who can offer the service faster than Tønder.

I would suggest the same to you as Ainos1912. What about asking the authorities in Sønderborg and Haderslev e.g.  Maybe, their calendars are not so crowdy. Sometimes, one can be lucky!