Sincere condolences on the loss of your father! Eternal memory!
While it may be best to let the Latin Catholic experts chime in on this specific arrangement, I would start by telling you that in the Eastern traditions it is more the norm to have the Rite of Christian Burial without a Mass (Divine Liturgy).
What is most important is that he is respectfully remembered in prayer as he goes to his eternal rest, especially by those who love him the most.
In my tradition, we normally have a prayer service at the funeral home, which reflects on the history of Salvation from our Creation right up to the moments just before the glorious Resurrection. It is a reminder of the promise of eternal life, earned through the Perfect Sacrifice of our Lord, God and Savior Jesus Christ. Pray that your father now enjoys the eternal reward assured by Christ’s victory over death, knowing that this is not the end of his journey, but the next step.
Prayers for you and your family! :gopray: