Use what you have, which is the SSKI. Dr. Jonathan Wright uses SSKI for skin, other people prefer Lugol's. If SSKI works, that's one less thing to keep track of.
It's hard to answer whether you need to take iodine with SSKI. The body is supposed to be able to convert at least some iodide to iodine as needed. I don't do that so well, and find it easier to take both Iodoral and SSKI. My mother just takes SSKI. If you have cystic breasts or ovaries, you might consider taking a molecular iodine such as Lugol's, Iodoral, even Iosol, to partner with the SSKI. Otherwise, leave well enough alone and know you can always change your mind later.