This is very much a pastoral decision that your pastor will have to decide. The following is my own opinions of what is possible.
The full Catholic funeral Mass liturgy is reserved only for Catholics, since the text has explicit reference to the deceased having been baptized and have received Holy Communion. However, there is nothing preventing the Church from providing a funeral service without Mass. This is essentially like a funeral Mass but with the liturgy of the Eucharist and Communion cut out. This is usually done at the funeral parlour, but may also be at the church. An appropriate form of commendation can also be done with the casket present, and interment to follow.
An alternative is a memorial Mass for the dead which does not have those explicit reference to baptism and communion. This is usually not a funeral liturgy, so the casket is not present. However, some pastor may allow for this being used as the funeral Mass. But this is highly unusual, and it will depend on your pastor.
My recommendation for you is to sit down with your pastor and explain your wish to him, and pray that God will provide the best arrangement through him.