You can buy a standalone 1st class ticket and not use interrail on that day.

It may be possible to pay an upgrade for your pass but depending on the rules on that railway it could be impossible or cost more than just buying the public rate ticket.

If you tell us the date and time there may be alternatives.

You can travel without reservation from Copenhagen to Stockholm if you go Copenhagen-Kalmar with Öresundståg, then Kalmar-Linköping with Krösatåget or any other regional train. From Linköping there might be a reservation free train directly to Stockholm. Otherwise you can take Mälartåget Linköping-Katrineholm and Katrineholm-Stockholm.

You can also check if you can get seats if you split your trip in 2. You can try Copenhagen-Linköping and Linköping-Stockholm

OR-even more easy-from just across Sundt/water-Malmö-are many more trains X2000 starting there-the very few direct fra KÖpenhamn are just like the direct DSB to Hamburg very in demand-plus that most people seem to have lost any idea in thinking for themselves and only look at the first planner spit-out.

Same as for direct TGV DE->FR/Paris-many more from just across Rhine=river/border from Strasbourg.

As @mcadv says. You can take Öresundståg to Malmö and look for a train from Malmö to Stockholm. 

Thank you so much for your answers We now have tickets from Copenhagen to Lund to Linköping to Katarineholm to Stockholm. To get seat reservations for trains requiring it we had to make reservations separately. And we managed to cancel the first class tickets s well.