The vast majority of OEM hubs for adult bikes are 3/16" front, 1/4" rear, usually ten per side in front and nine per side in back. Exceptions do exist, but if nine 1/4" bearings comfortably fit in the cup with little to no extra space, that's very probably what it takes.
Quando is a line of Kun Teng, or KT, one of the largest hub manufacturers. By doing enough homework, or maybe just emailing them a picture of your hub and asking what bearings it's supposed to have, or asking them if they've ever made any singlespeed/track rear looseball hubs with anything but 1/4", you may be able to get a definitive answer.
If one had to figure this out without any external information, it becomes a matter of making an educated guess based on looking at:
- How the different sizes of bearing mate with the profile of the cone
and/or cups. The radii won't be exactly the same, but they do
complement each other (a bearing engineer would put that better I'm
sure), and by knowing what's normal you can pick up on incongruities.
Also if a bearing's radius is way too large for the cup/cone, it will
be apparent by the fact that it's making contact at more than one
- What installing the different sizes does to the positioning of the
cone relative to the rest of the hub, i.e. whether any sealing will
be sitting at the right level and able to work properly, or whether
any of the race is exposed that one would normally expect to be hidden.
- Where the ball track (the line the bearings clear away in the grease)
sits on the cone race. If it's at an extreme end of the race's curve,
that's a sign of the wrong bearing size. Being somewhere near the middle is a sign of the correct size. Likewise, in some cases one would be able to make inferences based on where the ball track is falling in the grease relative to where existing wear lines are on the races.
All the same considerations, especially ball track, apply to determining appropriate replacement cones.
Wheels Manufacturing makes replacement cones for many common KT hubs. I have no idea if they'd be applicable to your track hub, but maybe.