Is a blood sacrifice required of one who entered into ihram for Hajj on behalf of his infant son and completed the rituals with him?

The phrasing of the question is problematic. If the intention is that the son is four months old, then your performance of Hajj on his behalf is permissible. You would perform the rituals for him and keep him away from the prohibitions of ihram (definition). There is no harm in your entering ihram for him on the afternoon of the Day of Arafat, as long as you fulfill all the pillars and obligations on his behalf. However, if he reached puberty four months ago, then he must enter ihram for himself and perform all the rituals himself. It is not valid for someone else to enter ihram on his behalf. If he enters ihram on the afternoon of the Day of Arafat, his ihram is valid if he performs all the pillars and obligations of Hajj.