My cousin's daughter in law showed up to his mother's funeral wearing a black, strapless cocktail dress, black ankle strap stiletto heels and a little black "Fascinator" hat. That was inappropriate.

Things are a lot less strict than they used to be.

Wear something 'formal' enough to indicate your respect, but don't worry too much about it being all-black or a skirt or dinner jacket or whatever.

helpfully,
Bright

But if they're very conservative Catholics it might be a nice gesture.

If you're unsure, take along a scarf or something you can put on if it looks as though everyone else (female) is covering.

For the most part, though, the "women cover your hair" thing has been dying out in white Catholic congregations since Vatican II. I believe some African-American Catholic church congregations still go with the "church hat" thing.

helpfully,
Bright

Just show up and follow what other people are doing. Stand when they stand, sit when they sit.
You can remain seated when others go up the aisle for communion.

These days people wear pretty much anything, but I still wear a dark dress or a skirt to a wake or funeral. And the standing, sitting, kneeling can be confusing, but just follow what others are doing.

And it's been a long time since women wore hats. I remember when I went camping as a kid with my Girl Scout troop, and since it was associated with the nearby Catholic Church, we were expected to go to church on Sunday. I remember that the leader pinned a Kleenex to her head since she hadn't brought a hat - but that was back in the '60s.

Nice blouse and pants are also acceptable. Basic office attire is fine.
Dark color is preferable (black, gray or brown) but not essential. Just no happy colors.
You can sit when others kneel, but always stand when the others stand.
No need to go up to communion. You can sit or kneel when others going up to communion. If you sit, sit about six inches from the back of the pew in case someone behind you is kneeling.

You will see others genuflect when they get to their row (kneeling, crossing themselves) before they sit down. You do not need to do any of this.

sloppy (and I know you won't), and of course, console if possible the family and friends there, perhaps offer a good story that includes your deceased coworker, if possible. They would appreciate it.

I'm am so sorry to hear of your coworker's passing, perhaps other coworkers will be there too and share in your sorrow too. It's always a sad thing to hear of former coworkers passing on.

Peace.

If this is American Roman Catholic, it's not too big of a deal. Dress appropriately, doesn't have to be all black or anything, but shouldn't be too "loud". When everyone stands, stand up. When they sit or kneel, just sit. There may be a few rows up front reserved for family but otherwise sit pretty much anywhere. You won't be the only non-catholic by a long shot. You may even be in the majority.

Are you allergic/sensitive to burning incense?

Listen to the priest or watch the others on when to sit,stand or kneel.
If you don’t wish to receive communion, you don’t have to get in line to see the priest, just stay in your pew. It more important that you are there for friends and family.

You might also want to sit during the funeral Mass; only Catholics sit, stand, and kneel when it's called for. Non-Catholics can sit during Mass without being disrespectful.

And do not go up to receive Communion if you're not Catholic.

you obviously haven't been to an Holy Communion in the Episcopal Church.

The Episcopal church doesn't discriminate against LGBTQ people and women like the Catholic Church.

It is the Protestant Church which is closest to Catholicism. It was founded after Henry VIII of England broke with Rome over a number of things, such as the annulment of his marriage to Catherine of Aragon, which he didn't get for political reasons.

I can post on it if you like.

to funerals.