It does amuse me that so many people are insisting that there way is right and the other way is common/wrong/American etc.
It seems to me that both ways are right, or common/wrong/American etc. My way is sha, and from where I stand with my rather posh relatives (landed gentry, minor aristos) that's how it is and always has been.
When she is introduced, she will be introduced using the pronunciation you use. initially, the people you introduce her to will hear Felissia and that's what they'll say.
Who cares how the Registrar pronounces it?
Teachers will quickly learn the pronunciation you prefer, and judging from this thread, lots will pronounce it your way anyway. Same for doctors and hcps. Friends and family will go by the sound not the spelling.
Basically, it's a non-issue.
But the thread's been fun 