You have to smack the bejesus out of a cast iron sink to break it! You would surely damage the countertop.
A still but flexible putty knife cna probably be slid under the edges, being careful to not scratch the formica. It will be difficult to get under the back edge.
I don't know if you can get any caulk remover (available at the hardware stores) under where the caulk actully is.
In the end, you do run the risk of lifting the formica. It is just a chance you have to deal with.