All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The fiancée is a stranger to her suitor. He is allowed to see only her face and hands while proposing to her and without being alone with her. The proof for this is the Hadeeth reported and authenticated by At-Tirmithi on the authority of Al-Mugheerah ibn Shu’bah, that he proposed marriage to a woman and the Prophet told him, “Look at her, for that will make both of you more intimate with each other.”
They should not, however, touch each other. Al-Khateeb Ash-Sharbeeni said: “Touching the fiancée is ruled out by the permission to have a look at her. It is therefore unlawful to touch her, because there is no need for that.”
You should explain to your father that it is not permissible for him to ask that you touch your suitor or allow him to do so, for there is no benefit in that. It might also cause violation of an Islamic injunction.
The correct way is that you look at him and he looks at you. If both of you are satisfied with each other, your father can then marry you to him in the presence of two trustworthy witnesses. Then the marriage is complete.
Allah knows best.