What the guys said above, and also it's only weird if you make it weird. Just ask, just say it, be confident in what you want, they'll either do it, or not. Treat it the same as any other requirement for that role.
But if you're hesitant, if you're apologetic, if you won't just come out and say what you want, the actors will sense that and you will come across as creepy.
There's always a chance. How your NLE handles it will vary.
I'm not an expert but here are some ideas. I'm assuming you all work within a few feet of each other. All require to share your G-Speed Shuttle in System Preferences / Sharing.
1. Depending on your companies IT setup, sharing the G-Speed Shuttle as described above may allow your co-workers to access it through the company network. Their access would be much slower than yours.
2. Buy an inexpensive networking switch, $10, and run your own ethernet to each Mac, use wifi to connect to the company network. If you already use ethernet to connect to the company network you may need Thunderbolt to Ethernet or USB to Ethernet adapters.
3. You can use Thunderbolt to connect the Mac's to network with each other. Your Mac would need two Thunderbolt connections, one to the Shuttle, one to a coworker. And that coworker would need two Thunderbolt connections, one to you, one to the other coworker.
Not sure about the adapters, but a huge positive vote for Filmic. That app is amazing. Make sure you get an iPhone with lots of memory, the higher bit rates create huge files. I did a 10 minute 4K recording and it was almost 6 GB.
There are some hits that you can get relatively inexpensively. SongFreedom.com has artists you've heard of (Bob Dylan, The Lumineers, Lady Gaga and others) for $60 for a wedding video.
My feedback, take from it what you will. I am by no means an expert.
Notes as I watch:
10 minutes is a long time.
Lots of handheld, everything shouldn't be handheld
You start with this big sweeping song, but your shots don't feel the same way. There's no slow motion, no big sweeping movements that match the song.
At 4:46 there's a guy that walks in front of the camera, then the photographer behind the bride. Cut to something else, get him out of there.
Movements and matching get better during the ceremony, I still think you could use some more slow motion.
Framing during the ceremony could be improved, heads are being cut off on the couple
6:30 that shot looks amazing, why is it so short?
The color looks off during the first dance.
7:51 going from the slow song to the fast dance song is really jarring
It's dark during the fast dance song
Showing the food at this part doesn't make sense to me
Until the wedding party starts dancing the fast dance song doesn't fit the visuals
Make it shorter. I know there's a lot of shots you probably like, but they don't really move the story forward. Especially in the getting ready and between the first dance and when the wedding party starts dancing.
Invest in some lights, a better camera in low-light, or learn better settings on your camera. There's a lot of shots that are really dark. They don't look purposefully dark, they look mistake dark.
Get or use a tripod or even a monopod. Lots of shots are shaky in a way that doesn't add anything.