1) wearing kippah is a minhag (a custom).  There is no mention in Scripture of Yeshua ever wearing a kippah (of which I am aware).  It does not appear that it was His custom so we have no example in Him to follow by wearing kippah.

2) wearing kippah is only a requirement (from a Talmudic perspective) during prayer which happens to be when I wear a kippah during the week... during afternoon prayers.

No definitive answers... just a bit of information.  :)