I have tried in the past to have my mother write down her wishes concerning funeral arrangements. She has always resisted, and often changed her mind as to what she has told me she wanted. However, due to a recent death in the family and seeing many issues that can arise, she now has said she wants no funeral service. Before I sit down with her to actually have something put in writing, I would like to get some input. I know she does not want a wordy obituary about her life, so alternate "life celebrations" is not what she would want. But just saying the deceased requested no funeral services seems rather stark. (And it may turn out that mother does want some kind of service.) How should this be worded for a death announcement? If other family members are very disturbed with foregoing traditional services, what could be simple ways to honor her without going against her wishes?
If she does choose to give you instructions - and don't badger her about it, it's in poor taste - follow them (and without looking for loopholes, by the way).
If she doesn't, then her executor or her next of kin if there is no executor should make the arrangements s/he thinks best.
As noted by others, the funeral or memorial service is mainly for the benefit of friends or family. It helps them heal. Remind her that many people would just like to have a way to say "goodbye". Is there anything she could suggest?
No one would want to include something the departed would find disagreeable. If she doesn't want clergy, OK Mom, we don't need clergy. If there is some kind of music she objects to, OK Mom, we don't have to have that. Flowers? Not necessary. A number of traditional trappings could be dispensed with. A bit of gentle questioning of your mother might suggest some ways to mark her passing in a dignified, sensitive way that she would not find objectionable.