Easily. There are plenty of taxis and "tour guides" right there at the dock where the tenders dock. GC is one of the safest and easiest ports to do things o your own.
You may wish to get on the internet and search for Grand Cayman tour companies and reserve a tour guid for a group as large as 8. Just so you know you are covered. It is still be cheaper than the cruise ship tour as you are not paying the cruiseline's cut.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013