What should a girl do regarding a Christian young man who wishes to embrace Islam and marry her, given her fear that her refusal might be a reason for him to distance himself from Islam and that she would bear the sin for that?

The relationship between the sexes is forbidden and is a source of temptation and corruption. You must cut off the relationship with the man who wishes to embrace Islam and marry you, even if he converts. What happens to him afterward will not harm you. Take the initiative to leave the websites he frequents and change every means by which he can contact you, as an act of repentance to Allah and a caution against His wrath.