There are very expensive $250- $300 chargers that do higher than 6s, probably closer to 10s, but not a lot to choose from and right now my memory is drawing a blank on their names, but they do exist.
I have no idea why there are not more, but I suspect that the demand is simply not there yet. Lithum batteries at those higher voltages are not as common and can be very expensive as are they chargers.
The charger you link to balances its battery by having a charging connection and balancing connection at the same time. The charging connection is directly connected to the + and - of the battery and supplies the main charge. The other connections are more complicated and, for example, in a 6s battery there would be 7 connections, one at the "-", on at the "+", and a connection or wire coming from every single cell connection. So each time another cell is added to make it a 2s or 3s, a wire comes out between the "+" and "-" of each cell added. So a connection between all 6 cells and one at the botom or "-" and one at the top or "+" and you have 7 wires coming out that will then plug into the side of the charger.
The charger then monitors each individual cell's voltage as it is charging the battery as a whole, but most chargers don't seem to start balancing until the battery is essentially full, or at least one cell is at 4.2 volts. Then it uses the seven wire connection to balance the battery, usually by discharging the higher voltage cells a little via a small current, and then charging the whole battery again slowly. Then repeat until all balanced.
It looks like what you linked to would work, except that they are for smaller number of cells in series than what you want to do.
Another option that would work for you is to do what you are doing - split the 10s into 2 5s and charge them independently, but parallel charge them using a parallel charging board and then you could charge them at the same time.
Check this out: http://www.hobbyking.com/hobbyking/store/uh_viewItem.asp?idProduct=14856
Yes, it is feasible. You just need to expose the balance plug and main positive and negative terminals (using a socket that cannot be accidentally shorted out or have something inappropriate plugged into it).
One possible problem is that the charger detects a full battery by monitoring the charge current and shutting off when it reaches 1/10th of the programmed current. At the standard charge rate of 4A the charger expects to shut off at ~400mA. However if your load is drawing 500mA then the charger may not properly detect the end of charge. While this won't damage the battery, the charger could run for longer than it needs to. Luckily your charger has a safety timer that can be set to 1-120 minutes (90 minutes should be plenty long enough).
You can charge through the balance connector by paralleling the positive and negative balance wires (red and black) with the main charger outputs. However the balance plug and wiring is only good for low current (<2A) so the charging time will be longer.
Note that during charging the battery voltage will reach (or even slightly exceed) 8.4V for quite a long period of time. Make sure that your load can handle this.
Best Answer
That will not work.
Not without extra care, attention and electronics.
If one cell when you start charging is 3.3V and the other is 3.4V, depending on the quality of the cell and thus its internal resistance, already you can have a situation where one cell forces several amps into the other the moment you connect them in parallel. Doing this regularly will severely reduce the life of your batteries. If the difference is larger the currents can be big enough to cause serious and immediate problems.
Apart from that, you should be aware that your device or pack should turn off the current drain once either one of the cells falls below a safe minimum voltage (3.2V for example, or 3.0V), so that they can't discharge to a point where damage occurs. This is why many 2cell packs have an internal BMS board that monitors both cells for over and under voltage and turns them off if either is at danger.
With home-made wearable tech I'd also strongly suggest you add current-limit protection inside the battery pack, so that a single mistake while wearing has a much lower risk of short-circuit based fire and/or injury.