Hi Ray,
You are correct about the AA's being the proper battery but this is when using the standard battery holder and this is not what is in the rechargeable pack. Whites does indicate AA rechargeable batteries can be use in the standard pack, though.
Now, I suspect the factory rechargeable pack does use the sub C. That would make sense. So, they use two different types of batteries, one for the regular pack and a different one for the rechargeable batteries. The use of sub C rechargeable is common for a lot of equipment from drills to metal detectors simply because they have high current rating yet are quite compact.
Now, as for rebuilding the rechargeable pack, one could use nicads or NiMh but it might be best to build up a new set using all the same batteries. If the original battery pack is not terribly old, chances are NiMh batteries were used. If it is an older pack, it is possible it could have NiCads. Maybe we could find out from Whites at some point when they changed.
It probably isn't a good idea to mix the two when building a pack if possible. I am not sure just what would happen because the charge rates could be a little different. It could work just fine or there could be problems. So, it is something to keep an eye on. Remember, when charging a 12V pack, all a charger generally does is provide a voltage greater than the pack voltage. The charger is limited to a maximum charge rate also to help protect the batteries. So, this will minimize problems.
Now, I do not know how many sub c's are used but assuming it is a 12V pack, there may be 10 since the typical voltage of a NiMh or a NiCad is 1.2V at normal operation. They charge to a little over 1.5V but quickly drop to 1.2V during operation.
Here is something to keep in mind, when charging NiMh or NiCad, when the battery starts to get hot, it is nearly fully charged. So, when the pack is getting hot and has been for a while, it is a good time to stop the charging cycle. Older batteries could suffer more from overcharging than the newer ones, but even the new ones don't like excessive charging. Over charging can lead to the battery venting gases which ultimately reduces the life of the battery.
Option C is to do what was also recommended and that is buy two sets of rechargeable AA batteries and keep both charged and use them in the regular holder. Rechargeable AA's will not last as long as the factory rechargeable pack but should work fine.
Now, there are rechargeable Alkalines also just to confuse things. One advantage of these batteries is the fact they don't discharge over time like the typical NiCad or NiMh. To further compound the issue, there is a newer special NiMh that is sort of a cross between the NiMh and the Alkaline and these don't lose their charge nearly as fast. It is almost act like they are regular batteries in terms of discharge but do reduce in voltage like typical NiMh's. Generally, the NiCads work well, but have less current capacity than a NiMh, so they do not last as long as a typical NiMh battery.
For those interested, here is a link to a brand of rechargeable alkalines. The link provides some interesting information you might want to know. As an example, the warmer a NiCad or NiMh is, the faster the self discharge rate. So, if you are going to be out for a few days, it might pay to toss them in a refrigerator or cooler but make sure they are kept dry.
http://aphnetworks.com/review/pure_energy_xl/xlaa_tds.pdf
An important bit of information for those of you who don't visit the site is the amp capacity of the battery at different discharge rates. What this simply tells us is the higher the current drawn the shorter the life because the actual amp capacity reduces. So, if using rechargeable alkalines it is a good idea to use headphones to extend the battery life. My guess is if you rely on the speaker, the battery life will be between 1/2 and 3/4 of what one might get using headphones.
Sorry to be so long winded.
Reg