Ok, so I have tried adding a custom keybinding so that Control+n does the copying:
(keybinding "c:n"
(lambda (editor evt) (send editor copy)))
Works perfect, but conflicts a bit with my muscle memory.
So I tried adding a custom keybinding using c:c, and now when I open DrRacket, I get the error:
<<Error when installing the keybindings /home/dimaugh/prog/rkt/keybindings.rkt:
map-function in keymap%: "c:c" is already mapped as a non-prefix key>>
But after clicking the OK button I can use DrRacket, and Control+c works as it should.
The error message bothers me a bit, but other than that it's now solved.