What would I do?
Well if I were flying into Heathrow I would order some Norwegian krone from travelex to pick up at the airport and have it ready for that part of the trip because I know I could spend it when "on my own." I would not worry about the Danish day until I got off the boat and ask the tour guide what is best to do bearing in mind you like to tip for good service, not that you're explaining why you have no change. If they are worth tipping they will answer you in a way that doesn't make you feel stupid or rude. Take some dollars in case they do accept those, be ready to pop to a cash point if an opportunity arises but most importantly don't worry. You're on holiday. You've booked a tour to make things easier not more complicated.
I've seen buskers use contactless things to make it easier to get money. If I worked with tourists I'd set up apple pay, PayPal, anything that would make it easier. They might not be of the same mindset though.