A lady’s cousin is not one of her mahrams (non-marriageable relatives). So, if there is a need to come in front of him, she has to be in her full hijab.
Hijab stands for the appropriate clothes that covers woman’s body and neither reveal nor shape the body and are not seductive in themselves. Islam blocks means to evil and temptation. So, Muslim ladies are not allowed to unnecessarily mix with non-marham men of all all kinds
It is noteworthy that People need to change and reshape their traditions to make them in conformity with Islamic teachings. Leniency in mixing between male and female relatives has caused a lot of temptations and troubles that could have been spared, if Allah’s limits were observed.