Our new priest does not wash his hands at offertory in daily mass. He says without a server it is hard and the rite no longer has practical use. Is this right?

The priest celebrant should wash his hands, even if there is no server. Though it is a bit awkward to pour water over one's hands from a cruet, finger bowls can perhaps be used for the purpose. 
 
Father's explanation that there is no practical necessity for him to wash his hands does not hold. It is true that the hand washing in ancient times had more practical purposes due to the reception of many and varied gifts during the offertory procession. Handling these things often soiled the priest's hands. But liturgical rites don't have a merely practical point. The washing of the priest's hands has an important spiritual dimension as well, indicating his desire to be free of sin before offering the Holy Sacrifice, and handling the Body and Blood of Christ. Omitting this rite is not permitted.