You will probably need to replace the masthead sheave to one that fits rope. The profile of a wire sheave is different, and may be too rough for rope.
Today's Dyneema, Spectra, and Vectran cored ropes are quite strong, and less stretchy than wire, with a polyester cover to equal UV resistance.
You could look up the breaking strength of your diameter and wire construction, and then check the breaking strength of high tech lines, and I'm sure you'd find that something thinner than 7/16" would work.
I looked very briefly, and 5/32" 1x19 SS wire is between 3000# and 3300# breaking strength. Then, I looked up Yale Crystalyne's (Vectran core) "tensile strength." 3/16" is 3000#. 7/16" is 15,200# Even stretchy New England Sta-set polyester double braid 5/16" has 3,500#
You might want to touch base with a rigger...