If one must walk 4 Amos in his home and doesnʼt have something with which  to cover his head, he may do so with his hand .However, if one is outside (and he is directly under the sky) using his hand for a cover will not suffice.

2) If one is in a place where he cannot cover his head (like a court house, where it may be the law of the land that heads must be bare), or if he is in such a profession that he is afraid that covering his head will cause him loss of clients or revenue, there is a possibility that he can walk with a bare head without transgressing this Halacha, due to Dina DʼMalchusa(law of the land).

 Yesterday we learned about not putting on two articles of clothing at once. The reason for not doing this is because it can lead to forgetting oneʼs Torah (Kashe LʼShikcha). This prohibition does not apply to women (according to most Poskim), as women are not prohibited from forgetting Torah. [However, from the texts of the Poskim it seems that they might however forget what they did learn if they do this, so any woman that doesnʼt want to forget any Torah that she has learned( especially from the Halacha For Today emails ) is wise to adhere to this Halacha even though she is not bound by the prohibition]

The Tzitz Eliezer based on the Aruch Hashulchan maintains that this prohibition does not apply to shoes [as they arenʼt considered clothing]. Therefore one may put on two shoes or a shoe and a rubber/ boot at the same time..