Cones and balls

I am trying to make a bike on a budget and would be grateful if someone can help me with a question about cones and all bearing sizes please so I can save a set of wheels.

The wheels have no name hubs and a cup and cone set-up. Solid 9.5mm axle. I've taken the rear axle out and the cups are fine. The ball bearings are 1/4 inch size (6.3mm diametre) and there are two sets of nine in the rear hub.

One of the cones is a bit rough and I'd like to replace it but I can't find any other sizes except 3/8 and 5/16.

As there must be literally millions of these hubs with 1/4 inch balls out there, it is a bit strange I can't find the associated cones.

Alternatively can I simply replace the axle etc with a generic part like this one and assume it will work with the cups?

https://www.halfords.com/cycling/bike-parts/bike-wheels/halfords-9-5mm-x-175mm-axle-with-bearings-and-grease-chrome

Can anyone suggest a solution? Thanks in advance.

Any other info.
Hub make/brand model, old or current in case you have a weird one with brand quirks.

Have you checked SJS for cones..... https://www.sjscycles.co.uk/other-hub-spares/?page=5

They are singlespeed disc brake hubs. I was told they were off a Genesis Day one but I'm starting to doubt that as the Day One wheels seem to all have cartridge-type bearings. There is no branding.

So I'd say they are pretty current and mass market. I can find references to the nine 1/4 inch ball rear hub configuration online so I don't think it's that unusual. I just can't find a corresponding cone, which seems bizarre.

I had a look at the Wheels Manufacturing site but they show the size of the cone but don't explain what size bearings it is for - this would be more useful I think!

Go to your local friendly lbs and ask to fish around in their spares - they’ll have loads of this kind of thing kicking around.

Shall consult Sheldon.

Not that much detail in the old testament of sheldon RIP

Cones are cheap and mass produced, i had a tin full of them and used to pick and mix.
Maybe avoid the really cheap axle/cone/bearing kits as i bent 3 solid axles from them, i suspect the Halfords quality is not that high, just the price, would give one a go though if stuck.

Howards right though, good LBS would have a box full of the things and should sell loose ball bearings to suit.
Take your axle and cones to LBS. The Wheels manufacturing parts are nice and you get quality parts that are better made than the rest of the set up :)

Older shimano rear hubs have 9 1/4" balls and 10mm axle (which can measure as 9.5mm because of the threads). Maybe get cones from one of them?

I think Shimano uses 1mm threading (so 10 threads pr cm if you want to measure)

https://www.rosebikes.co.uk/bike-parts/hubs/accessories/hub-cones-&-balls

It is probably cheapest to just buy an appropriate shimano rear hub and use the axle, balls & cones from it.

Ball bearing wise try and get grade 100 ball most bike shops I went to sold weldite balls that were either 1000 grade or if grade wasn't listed 2000.

Here is what the number mean.
https://en.wikipedia.org/wiki/Ball_(bearing)