Is a Muslim sinful for not shaking hands with his neighbor who wronged him, after his innocence has been proven and he desires reconciliation, contenting himself with merely offering salutations?

Your neighbor's actions of cursing and hitting you based on an unverified rumor constitute injustice and aggression. He should have verified the information, as Allah states: (O you who have believed, if there comes to you a disobedient one with information, investigate). Allah has encouraged forgiveness towards those who do wrong, as He says: (So whoever pardons and makes reconciliation - his reward is due from Allah), and as the Prophet, peace be upon him, said: "Allah increases a servant in nothing but honor by his pardoning." You have done well by forgiving him. Complete your good deed by shaking his hand to remove animosity and attain Allah's pleasure, for the Prophet, peace be upon him, encouraged spreading peace and shaking hands upon meeting due to the forgiveness of sins that results from it.