You can celebrate a funeral liturgy without the Eucharist. It’s not common in areas with available clergy.
177. In the funeral liturgy outside Mass the community gathers to hear the mesage of Easter hope proclaimed in the liturgy of the word and to commend the deceased to God.
178. The rite may be used for various reasons:
1. when the funeral Mass is not permitted, namely on solemnities of obligation, on Holy Thursday and the Easter Triduum, and on the Sundays of Advent, Lent, and the Easter Season.
2. when in some places or circumstances it is not possible to celebrate the funeral Mass before the committal, for example, if a priest is not available.
3. when for pastoral reasons the pastor and the family judge that the funeral liturgy outside Mass is a more suitable form of celebration.
What sort of special effort is needed to ensure a funeral outside Mass is an adequate expression for the family and community? Would it affect the choices of readings and prayers?
The only serious conflict I’ve ever experienced on point 1 of OCF 178 is when a funeral had to be postponed until Easter Monday. The family insisted on Mass. I suspect that the framers of the rite didn’t see this as a spiritual hardship. The assumption was probably that the family and friends would attend the liturgies of the Triduum. Like all of Christendom, right?
Finally, note that the pastor and family make the call on the appropriate liturgy.