We were on the Symphony from London to Rome, and my husband wore khakis with a collared shirt during the day for tours, etc. In Monte Carlo he dressed the same but with a blazer. While on the Atlantic where is was cool, both of us wore jeans. Once we got to the Med, we wore shorts and golf shirts on board during the day. You will see a variety of clothing. It wasn't unusual to see nice athletic warm-up suits. But at night it was dressy every evening. On casual and informal nights, women really dressed with men in jackets (usually with ties). I have heard dress varies as to the itinerary.
You didn't mention where you were sailing but you will have a great cruise. Our cruise with them was our best so far though we have two scheduled on Radisson for later this year.