Is holding hands between an engaged couple considered a transgression, and how can one atone for this sin after separation?

What you mentioned does not constitute an injustice that necessitates seeking your fiancée's forgiveness. Rather, what is incumbent upon you is to repent to Allah by abandoning the sin, regretting having committed it, and resolving not to return to it. If you repent, then there is nothing held against you, and Allah accepts repentance and forgives misdeeds.