The ḥijāb with paternal cousins

The answer – and Allah is the One who grants success – is that it is obligatory upon the man, in such a case, to lower his gaze from what Allah has forbidden him to look at. Likewise, the woman must lower her gaze and cover her nakedness (ʿawrah). And it is obligatory upon both of them not to meet together in a place where they are alone and away from people.
She is not required to cover her face; rather, what is obligatory upon both the man and the woman is what we have mentioned: lowering the gaze and covering the nakedness. She incurs no sin in uncovering her face; rather, what is obligatory upon the man is to lower his gaze, and upon her to lower her gaze.
However, beyond that it is obligatory upon the woman to remain settled in her home and not to display herself with her adornment. Allah, Exalted, has said: “And stay in your homes and do not display yourselves with the display of the former times of ignorance.” [al-Aḥzāb:33] And He, Exalted, has said: “And let them not display their adornment except to their husbands…” until His saying at the end of the verse: “And let them not stamp their feet so as to make known what they conceal of their adornment…” [al-Nūr:31]. She incurs no sin, from all of that, in uncovering her face and her hands; that is not among the reprehensible matters. What is obligatory upon the man is that he lower his gaze.
The reprehensible matter which is not permissible for the woman is that she uncover her forearms, or show any part of her hair, or show her neck, or display her adornment, or leave her house and expose herself to men without need.
As for kissing and handshaking, it is not appropriate and it is not permissible; for when Allah, Exalted, has forbidden looking, then a fortiori He has forbidden kissing and handshaking.
And know that Allah, Exalted, by what He has legislated and commanded of lowering the gaze, forbidding display of adornment, remaining settled in the homes, and that they (women) are not spoken to except from behind a veil – by all of that He intends to block the avenues of immorality and to cut off the road upon Satan. On this basis it is necessary to abandon everything that calls to immorality. Among that is what the poet said:
A look, then a smile, then a greeting,
Then speech, then an appointment, then a meeting.
And handshaking, kissing hands, letting the conversation run on, and joking and laughing together are among the things that call to that.
Yes, if a person is tried with something of that, or there is a need for something of that, he must restrict himself to the extent of the need: such as speech, in which he restricts himself to what necessity requires and does not let himself go in what there is no need for. The Messenger of Allah (May Allah bless him and his family and grant them peace) used to speak to women and they used to speak to him. Among that is his conversation with the woman from (the tribe of) Khathʿam at the time when he was going to stone the jamarāt, and al-Faḍl ibn ʿAbbās was his rider behind him. The woman asked the Prophet (May Allah bless him and his family and grant them peace) about certain issues and he answered her, while the Prophet (May Allah bless him and his family and grant them peace) was, at that time, shielding al-Faḍl from looking at the woman with his cloak.
As for looking, then nothing of it is permissible except to the extent of need – such as for a witness, or a judge, or a doctor, and the like. As for other than a need, then it is not appropriate; for that reason the Prophet (May Allah bless him and his family and grant them peace) covered al-Faḍl ibn ʿAbbās and prevented him from looking at the Khathʿamī woman who had asked the Prophet (May Allah bless him and his family and grant them peace).
And if the situation forces him to handshaking, then he should wrap his hand with the end of his shawl or the like, and avoid as much of all that as he can. With sound intention and the fear of Allah, Exalted, Allah will grant him a way out and relief, as He, Exalted, has said: “And whoever is mindful of Allah, He will make for him a way out.” [al-Ṭalāq:2].

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2