there is no requirement that there be a funeral Mass. there is a provision for a service, which can be presided over by a deacon in the church, with or without the body present, or at another site like the funeral home, again w or w/o the body present, and a committal service at the gravesite. also wake service of course. there should be some kind of rite associated with the commital and burial. if there is to be cremation, there can be either a funeral mass or service with the body present, followed by cremation, or a memorial mass without the body present, before or after cremation.
a lot of this is dictated by the cost of preparing the body and casket, and moving it to and from the funeral home to the church, then to the place of cremation or burial. that is why many funerals of poor people here are service only, without the body, because they cannot afford to pay the costs associated with bringing the body to the church.