I would recommend taking the Öresungtåg to Københavns H and transfer to the Metro and go to Nørreport. Then walk over the water along Nørrebrogade toward Nørrebro and there's a huge density of bike shops selling crap through great stuff. Last time I walked from Gråbrødretorv (where flat is) to PANUM, I went by at least 10 shops (it's not a bad walk and the weather has been great!).

https://www.google.co.uk/maps/dir/Gr...d55.693188!3e2

Edit: seems you can even go from Malmö Centralstation to Nørreport directly by the Öresundtåg. No excuse now