Which African member of the Commonwealth was never part of the British Empire or had any other constitutional links with another Commonwealth member?

Mozambique and Rwanda are Commonwealth members with no previous constitutional ties with the British Empire or another Commonwealth member.

Cameroon is also a member of the Commonwealth and most of Cameroon was a French Trust Territory. Upon gaining independence it united with the smaller British Trust Territory of Southern Cameroon and joined the Commonwealth. This it does have constitutional links to Britain, in part.