As a starting point, you do not need cash.
You can use credit card everywhere. However, I would recommend a contactless card - alternative chip. Magnetic stripe only works in a few machines in hotels and restaurants. ApplePay on mobile phone will also be a good solution.
Best is MasterCard or Visa. Amex is not that widespread.
I have not used cash for several years in Denmark, Norway and Sweden.
Also note that tips and VAT are in all cases included in prices - also in restaurants.