Timorously is the adverb from timorous: doing something in a way that shows fear and a lack of confidence. It means much the same as 'timidly', but it belongs to written, literary English — you find it in novels and older prose, and it would sound strange in everyday speech. It attaches to small, careful actions: someone steps timorously into a room, speaks timorously, timorously reaches out a hand. The picture is of a person moving as though the floor might give way. It can also describe how an organisation acts, and there it is a criticism: 'the committee moved timorously' means they were too cautious to do what needed doing. Because it is rare, using it makes a sentence stand out — which is useful once in a chapter and tiring three times on a page. In modern writing 'timidly', 'nervously', or 'hesitantly' will carry your meaning without drawing attention to the word itself.