It's possible to order an extra code display dongle - that's priced at DKK 41.75 (incl. VAT...).
There's also the possibility of ordering a second one for free under the pretext of the first one having been lost or broken, but I'd assume the first one would be blocked in that case.
Edit: My solution going forward, having been without anything but the dongle for months, will be to install the app v. 73 in a secondary profile to supplement the dongle.