What is the proper dress for a Greek Orthodox funeral Trisagion?
Coat and tie if your a male. A long dress and head covering if you’re non-male.
It would be more prudent to keep the head covering in your purse, many Greek parishes are pretty Americanized and consider the head covering old school, on the other hand, many still do continue. Just go with the norm.
I think a head covering would be quite proper.
I have never seen a woman with her head covered in a Greek church. But in a Russian ROCOR church women must wear their babushkas.
But it is an act of obedience and piety to wear a headcovering. If the OP is female and so desires to wear one out of a wish to observe what St. Paul says to do, would not discourage her. Of course, if the OP is male, I suppose it’s a moot point.