Sometimes those things get a honking hum and throb to the noise because the blades are hideously greasy with gobs of dust sticking to them. Might check that first.

Don’t know if it would impact your situation, but I have seen a number of older installations (late 40’s/early 50’s as retrofits in older homes (1920’s, etc.) where the “duct” was actually the deadspace in the overhead between two joists. YIKES! I’ve never heard of a grease fire up in one of those, but they scare me silly worrying about that…if I had a setup like I just described, I’d stick a plenum up in there and run a muffin fan, hiding the mess with the original grille. Just a thought.
Dave

PS-We have a fan, but it just means the grease sticks to the overhead ceiling and everything on the way there. 6 to one, 1/2 to the other, maybe!

Check a good-size industrial hardware store, you will often find blade-fans in multiple diameters with multiple hub configurations “by themselves, on a plate” as I like to say.

If there is no place near you like that, check out Grainger Industrial on-line or also McMaster-Carr. You’ll probably find something that wil work, or maybe just look at used fans in the ReStore until you find one with a blade-fan that will do.

If the thing is a lost cause, i.e. you cannot find a blade-fan to fit it at all, consider hiding a muffin fan in the existing duct path. Could be a challenge to duct and wire (or not), but you would have a quiet, high-efficient fan and still retain your vintage fixture.

Good luck,
Dave

If the cover had some sort of center-mounting affair viv s vis a hole in the middle, find some sort of finial you like and attach it with a machine screw or bolt from the other side.

The “new” cover can be refinished if need be. There are lots of fairly convincing spray paints on the market, and if you do a good job no one will be wiser. If you are looking to replicate a chrome finish, be glad it’s up on the ceiling. If you are looking to replicate an anodized aluminum finish, try Hammerite if you can find it, or look at Rustoleum HardHat.

You can mount the new retro slight-oversized cover with corner mounting screws. Oval-head Philips-type sheetmetal screws would be appropriate, get stainless or if you really have to have shiny chrome…there are sources if you look around.

To look right you need to have a countersink for the screws, and since it’s sheet metal that really means a dimple as there isn’t adequate metal to really cut a countersink into.
There are purpose made dimpling tools in the sheetmetal trade, maybe a sheet-metal shop could do it real quick on the lunch break for a tenner, or…here is a low-volume way to dimple sheet metal up to about 16ga. maximum. I’ve done this many times and it works well:

Take a piece of HARDWOOD dowelng, about the diameter of closet rod, and clamp it in a bench vise with one end sticking up a couple inches past the jaws and the other end resting atop the sliding member of the movable jaw. If your vise is cheap and has an exposed screw, put a piece of scrap wood across there to try and spread any loads. Clamp the dowel in TIGHT.
Drill a hole just large enough for your screw to pass into without friction more-or-less centered in the end of the dowel.
Take a countersink, or failing that, a drill bit that looks right, and go to enough depth to JUST seat the screw head. Good. Now go a bit deeper, to just make up for the metal thickness of the part you want to dimple. This is your new dimpling die. Now layout and carefully drill the pilot holes for your screws in the corners of the grille.
Use a screw to line up the hole in the grill with the hole in the mandrel, and have a helper hold the grille right there. DO NOT be tempted to smack the screw with a hammer, you will wind up thrashing the grille! Take a large-ish centerpunch that happens to match the taper you want, or a bolt that you have ground to profile, and use that as the mandrel. Center it on the pilot hole, tap-tap-tap (as opposed to WHUMP! BANG! OOPS-SPLIT THE METAL!) with a hammer, and there is your pretty dimple.
Really easy and simple, the only thing to be sure of is that your tapers match.
Mount your grille and smile, right?

For noise considerations, I really like inline “muffin fans”. You will use a duct box in the ceiling and then run dryer-type hose to a remote, inline fan. The fans are not forever, so try to put it somewhere with service access available without cuttting things apart, right? You can run a LOT of duct length and still have PLENTY of suction, and QUIET. Nice.

Right over the bath or shower is a great idea to me. I also like the idea of a seperate “F**t Fan” NEXT TO the toilet in the wall. I’ve seen this in a lot of older houses and it makes great sense to me.

I have also always wanted a HEATED bathroom mirror so it wouldn’t steam up while I’m shaving. Gotta be a way.

Dave