It would be hard to do all that in 7 days. You might look at Costa or MSC. They may have some short excursion type cruises where you could cruise back to Rome from Sicily. You might also look into ferries, many are overnight. Not quite the same as a cruise but it will get you on the water. Alternatively you can look for a 7 day round trip cruise that uses Rome as the home port.
A Bad Day At Sea [with power] Always Beats A Good Day At Work
Alaska 2014 - haven't picked a cruise yet
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012
Celebrity: Summit 2011
Princess: Ruby 2010, Caribbean 2013