I think owning foreign currency in NK is probably grey-market normalised at this point. However I imagine it's predominantly RMB and USD. The requirement that everything be done by foreigners in Euros is probably serving the purpose you state though. I suspect authorities might look the other way at foreign currency in general, or specific currencies like those I specified, but Euros might be taken as evidence of unauthorised contact with foreigners since there's no other good reason to take them.
Interesting fact: the DPRK used to issue three parallel sets of coins and banknotes. One was for locals, one for visitors from other Socialist states, and one for visitors from Western states.
The three-tier model was a little but unusual, but the idea of a secondary currency for foreigners was not that uncommon.
One other reason for it is to ensure "minimum spend" -- some countries required you to buy a certain amount of the foreigner currency at the official exchange rate as part of the entry process, even though the black-market rate for "local" currency was far more competitive.
If foreigners can only own foreign currency, and normal citizens can only own local currency, then it makes it a lot harder to bribe the locals!