Generalized Curl
Cross[{d@x/sx, d@y/sy, d@z/sz}, {f, g, h}[x, y, z] // Through] /. d[v_] h_ :> D[h, v]
Unsightly Unicorn
Cross[{d@x/sx, d@y/sy, d@z/sz}, {f, g, h}[x, y, z] // Through] /. d[v_] h_ :> D[h, v]