Don't try to advertise being a tourist can be the best advice for traveling safely. The #1 travel safety tip is to just wear minimum jewelry, casual clothes, and keep expensive cameras inside a discrete bag. Try to relax and look like you belong there. This will automatically make traveling safer.
Be especially aware of your safety in crowded areas such as local festivals, crowded tourist sites, markets, airports, and on trains and buses (also inform yourself about transportation in Scandinavia). In some areas, it can make sense to travel first class or to hire a guide, in order to improve your safety.
Keep your card in sight at all times, even in shops/restaurants while the charge is made. Destroy documents that contain your account details - don't just throw them away. Inform your bank of travel plans so a] they don't stop your card in the wrong place b] they can monitor suspicious activity.
Try not to use big wallets or purses. Keep enough money for your immediate needs in your pocket (zippered?). The rest can stay hidden on your body or remain in the safe in your hotel room. Have different forms of funds in different places. Remember to protect your flight tickets as well.
Apart from making life easier, a small grasp of the language will also help you to be prepared. Take a look Scandinavian Language Basics.
Never let go of your purse or shoulder bag. When you sit down, sling your arm or leg through the strap.
