Q. I am not shomer shabbos. Should I wear a kippah during the week when not in shul?
A. Horav Shlomo Miller Shlit"a pointed out, that you might not be a shomer shabbos yet, but you are striving constantly to come closer to Hashem and to keep more of his mitzvos. Certainly it is desirable to observe as many as you can and not being able to keep one mitzvah does not mean that you should avoid the others. On the contrary, fulfilling one mitzvah rewards you with another. Especially, the wearing of a kippah as the Talmud (Shabbos 156b) states; "Cover your head in order that the fear of heaven may be upon you".
Horav Miller also made clear that Shabbos is not an all or nothing mitzvah. You try to do as much as you possibly can, then gradually as the magnificence and profound significance of Shabbos reveals itself, you will strive for the rest.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a