Can testimony be refused in cases of assault and conflict, knowing that there are no other witnesses and realizing the worldly and otherworldly punishment that would result from such refusal?

Your friend is not permitted to testify for his maternal cousin's son, as this constitutes false witness, which is forbidden. Allah linked it to the abomination of idols, as He Almighty said: ﴿So avoid the abomination of idols and avoid false statement﴾ [Al-Hajj: 30].

As for testifying against an opponent, it is a communal obligation (fard kifaya) if there are enough witnesses beyond what is required to establish the right, and the owner of the right requests it, and the witness does not fear harm, due to Allah Almighty's saying: ﴿And let not witnesses refuse when they are called upon﴾ [Al-Baqarah: 282], and His Almighty saying: ﴿And do not conceal testimony, for whoever conceals it - his heart is sinful﴾ [Al-Baqarah: 283]. Testifying becomes an individual obligation (fard ayn) for someone who has knowledge if there is no one else to establish the right and its non-performance would lead to its loss, and the witness does not fear harm to himself, his family, or his property by performing it, due to Allah Almighty's saying: ﴿And let no scribe be harmed or any witness﴾ [Al-Baqarah: 282], and the Prophet, peace and blessings be upon him, said: "There should be no harm nor reciprocating harm."

Based on this, your friend must testify for the opponent if it becomes obligatory for him and he does not fear harm. He is permitted not to testify if it is not obligatory for him or if he fears harm from it. Mere fear of a bad relationship is not a Sharia-compliant justification for concealing testimony if it is obligatory.