Yes, I do know about the British series you're thinking of. I've run across it when I've grazed through Netflix's offerings, though I've never ordered it. My wife and I find that there are a few TV series we've enjoyed through Netflix because they are not sliced up with commercials. Viewed that way, they zip right along, with a pacing that's far faster than they appear to have when the commercials interrupt.
The wool cassock wouldn't be too much of a bother. It's a very light wool, much less "weighty" to the touch and scales than denim. It drapes and moves like a dream. I hardly know I'm wearing it. And, I've worn it in Texas summers, in Gulf humidity (a diocesan clericus in Houston), and it never felt hot.
But, I'd rather not wear it, since the garment itself -- though way over on the formal end of clerical clothing worn outside a worship service -- is still so rarely seen among Americans that it would likely register on their radars as costume, not a uniform. And, they might not even recognize it for the garment it is, if they've never seen someone dressed in one. Ordinarily, the clerical collar -- visible in a cassock -- would be a good signal. But, as you'll notice in my avatar, I have a lengthy, curly beard which covers the clerical collar completely. It's virtually invisible unless I tilt my head way back. I'm wearing a Roman-style clerical collar in that avatar, but it's well masked by the beard.
My wife is pondering if she should dress for one formal night totally in black -- shoes, hose, skirt, and high necked blouse (like a turtle neck) all in black. And, therefore, all the better to flash the diamond necklace and earrings I gave her for Christmas. I've seen her in that outfit, and the outfit really puts the jewels on high-beam! Plus, we'd match -- her glory in platinum and diamonds, my glory in her on my arm, along with my white beard, eyebrows, and hair. Satorially, we'd be a comprehensive match.
I just hope the Maître d' doesn't look at my feet. The shoes will be inky black, but they're going to be New Balance walking shoes, which my GP insists I wear for the various kinds of support built into those shoes, which support he insists I need. A second opinion from a podiatrst agrees. So, I'm counting on my wife's dazzling the Maître d' when we present ourselves for inspection.
I will appear out of uniform occasionally while on the cruise -- when visiting the sauna and/or pool, at the beach, or when my bride and I sally forth to wander through the shops off the ship. But for just toodling round the ship, clerical clothing is simple -- no decisions, and no one wonders why you're wearing the same thing all the time. That's the blessing of uniforms generally.