Who,
exactly, said this?
Because they are entirely incorrect.
I could use my cousin who used to be Catholic (now considers herself a non-Catholic Christian)
Regardless of what she considers herself, your cousin is in fact a Catholic and one who does not meet the canonical requirements to be a Sponsor:
Can.* 874 §1. To be permitted to take on the function of sponsor a person must:
1/ be designated by the one to be baptized, by the parents or the person who takes their place, or in their absence by the pastor or minister and have the aptitude and intention of fulfilling this function;
2/ have completed the sixteenth year of age, unless the diocesan bishop has established another age, or the pastor or minister has granted an exception for a just cause;
3/ be a Catholic who has been confirmed and has already received the most holy sacrament of the Eucharist and who leads a life of faith in keeping with the function to be taken on;
4/ not be bound by any canonical penalty legitimately imposed or declared;
5/ not be the father or mother of the one to be baptized.
as a “Christian Witness”… So instead of having a god mother, my daughter would have a Christian Witness.
No, your cousin is a CATHOLIC and therefore cannot be a Christian Witness, who is a non-Catholic witnessing the baptism.
If you were to have an actual non-Catholic Christian Witness, it could only be in conjunction with a Catholic sponsor:
§2. A baptized person who belongs to a non-Catholic ecclesial community is not to participate except together with a Catholic sponsor and then only as a witness of the baptism.
…Should I do it?
No.
Ask a friend from your parish or ask your pastor for a recommendation.