Front axle cone replacement - sizing
9.4mm major diameter means you have a 3/8" axle, which is sometimes even called 9.5mm. The thread on it should be 3/8x26tpi, which again is sometimes called 9.5mm x 26tpi.

All Shimano hubs have the Shimano name and a Shimano-esque part number on them, which for normal front hubs (non-generator etc) will start with "HB-". Shimano doesn't do rebrands. Also all Shimano threaded axle hubs use metric axle threads unless there's a prevailing standard otherwise, as in 3/8"x24tpi internally geared hubs, low-end generator hubs for shopping bikes, etc. So from the sound of it, it's not Shimano.

Things I will say straight off:


Some shops specialize in Dahon and might be able to make this very easy for you. If you had access to such a place, that could be a good way of cutting to the chase.
If you insist on matching a replacement yourself there are technical aspects to getting it right that are a little outside the scope of an SE type answer (or at least one I'm willing to write I guess.) There's a second edition copy of Barnett's floating around the internet. I'm not really sure of the legality so I won't link. I believe it was compiled from sample chapters and it's largely outdated at any rate. However, it does have their chapter on replacement cone matching, the principles of which haven't changed. Every other writing on the subject I've ever seen on the subject is overly pithy and misses some aspects. 
One of the key steps in replacement cone matching is testing that the ball track is occurring on the new cone in an appropriate spot. Usually this means nestled neatly in the curvature of the cone, not too high or too low. Barnett's covers this in depth. Any good mechanic will do this test when installing a non-factory replacement cone and not make any promises beforehand. The point is that ordering generic replacement cones online is pretty dicey.
If one really wanted to try ordering them online anyway, you need to find a way to match curvatures. What I would probably do is use a scanner to create a good side view profile of the existing cone and overlay it properly scaled in a graphics app with the side view product images of the various Wheels Mfg 3/8"/9.5mm generic front cones (which they call "Taiwan cones" since several of the dominant OEM hub firms are Taiwanese) I'd be looking at as initial candidates to choose from.


To answer your questions:


Cup and cone hubs typically have no real ability to handle different ball sizes or different numbers of balls, the exception to the latter being most hubs can either have loose balls or retainers with the same size but a lesser number of balls. You need a  front cone. All generic replacement front cones are for 3/16" balls.
The color of the axle is irrelevant. Some have a black oxide finish and some have different kinds of raw or polished finishes. Well kept axles have grease on them and good chromoly ones are very corrosion resistant anyway, so it doesn't really matter.
3/8" axles are one of the sizes where the same size axle is used on front and rear hubs in some applications. So it's not true that 3/8" cones are categorically supposed to go with 7x1/4" balls. 7x1/4" would typically imply a rear hub with a bearing retainer, and in such a hub 9 1/4" balls would typically work without a retainer. You need a front 3/8" cone, which basically all are going to be sized to work with ten 3/16" balls. One of the confusing things about this may be that the metric sized axle standards, which depending on where you look have become more common, use different diameter axles front and rear.


The practical thing to do is one of two things:


Read the Barnett's chapter, then find a shop that has the full range of Wheels Mfg 3/8" front cones and take what you have to go try to find a match. The Barnett's chapter will get into the sealing and length matching considerations, as well as how to transplant pressed seals etc. Wheels Mfg used to make a 3/8" Taiwan Cone kit that I believe is no longer available in kit form, but a lot of shops still have it, and the cones that it came with are all still available.
Fix your existing cones by grinding them with a drill and sandpaper. I've come to have a high regard for this approach since it can usually be made to work acceptably unless the cone is devastated, and replacement cones can be harder to obtain than they used to be. There are questions here about this approach.