If necessary for some reason an observant Jew can go without a head covering (yarmulke or hat) including when bathing. They are supposed to put on the yarmulke before putting their feet on the floor to start the day out of bed.
According to the Shulchan Aruch, a code of Jewish law, observant Jewish men are required to cover their heads and should not walk more than four cubits without one.
The distance between thumb and outstretched finger to the elbow is a cubit sometimes referred to as a “natural cubit” of about 1.5 feet. This standard seems to have been used in the Roman system of measures as well as in different Greek systems.
In one book about the Holocaust I read it said as some defiant Jews who were led up the wooden steps to a gallows one by one the Nazis they would try to wear a head covering. One took a hidden yarmulke and quickly put it on. The soldier punched him and took it off. He had a second one hidden in his clothes and put it on. The soldier hit him harder and threw it on the ground. Finally he had one more under and put it on in defiance just before his hands were tied and he was having the noose put on his neck. The soldier hit him in the head with a rifle butt and then they hanged him.
So who witnessed this story?
It's reported that one of the other condemned Jews standing on the gallows whispered to him, "Hey! Cut that out! You want to get us in trouble?!"
A little gallows humor to start the day!
Regards,