First of all, I would try to lube the fan, with seving machine oil.It should fix the noise and also should enhance the speed -> little better cooling. If that doesn't make it then i would try to source replacement.
I try to keep my retro HW as close to original as possible.

Also I would say that this kind of cable doesn't exist at least not now.

I think that you can lube such fans whole day and they will stay bad, because they were bad by the design and noisy even brand new. Use some slowdown cable is only workaround and its risk, but this better than that noise, before i can get better aftermarket cooler or risk is worth of possibility of killing card

Problem is this era, was that cooling budget for such cards, was usually very small, much less that todays when even coolers from low end companies, are quite good, because they probably calculated that is really main thing which can vendor do with card design from Nvidia /AMD and with good cooling they add some OC and have less RMAs.
Small fan with 2000+ cant be silent, even Noctua world fans leader can do that..

If retro as possible means noisy, im not interested, free bundled headaches from constant unpleasant noise, no thanks.. I like machine, which i not hate to sit by.

BTW some aftermarket better fans are available even back in era and there are some are high end cards with better cooling too..

If you don't solder, the easiest option is to use a universal VGA cooler that has a larger/quieter fan. You just have to check the hole mounting. Some of the aftermarket coolers offer a standard 3-pin connector which plugs into the motherboard or molex-->3-pin adapter. I haven't seen any with a resistor, but you could always use a fan controller (3.5 bay / 5.25 bay / PCI bracket rheostat) to control it without soldering in resistors.

I use this one a lot, which plugs into the standard small 2-pin connector if you want to retain the OEM power plug, but in some builds I have removed the pins from the connector and installed a standard 3-pin fan connector -- which only requires a tiny jewelers screwdriver to pop the pins out. (pins are the same size) There's no yellow 3rd wire for tach/speed, but it can still be controlled with a fan controller.
https://www.ebay.com/itm/Universal-43-50-53-5 … &frcectupt=true
or
https://www.ebay.com/itm/Golden-55-60mm-VGA-V … EC/362563504237

Also, I wouldn't slow down the OEM fan, because they usually have a small heatsink which requires a fast fan speed to prevent overheating.

I have this one too, main disadvantage is 2 or 3 slot with card, i not sure now.

Of course if have better cooler at home, i replace it, but i need keep card - 1 slot and i often have to (even my testing systems are usually quite crowded by cards), i simply not have good replacement which is compatible with paricular card and even i have it would be already used on other card.. So its better to risk it, is use such extension that wait month that some fan replacement arrive from eBay if available for order right now, often i have to wait.. and make some research etc.

Other important point is that in this era was typical that some cards, run fan at full speed all the time, even in 2D, at boot, in DOS, in Linux etc.. in late era at least some of cards, regulated fan speed when Windows drivers where loaded.

Other thing which i would like to buy, are these heatink holders, or that is right english name for them.., there are often missing, or half broken, i broke few of them by myself.

Update: Keyword for Ebay:- Heatsink Cooler Cooling Fan Spring Rivet Fastener Push Pin Mounting Screw // Master degree in Chinese English needed 😀

Yes, indeed...
https://www.amazon.com/1000pcs-Fastener-Mount … g/dp/B01LAVP462

PS is the fan you want to trim 5volt or 12 volt ?

[edited]

I can recommend this cooler:
https://www.ebay.com/itm/Golden-55-60mm-VGA-V … 872.m2749.l2649

Its surprisingly silent, only disadvantage is that is 2 slots and its not cooling anything else than my chip, but for 3 bucks its much better than others similar coolers.. for me its not final solution, but for some card which im occasionally using for testing is good enough.