Hi;
yes, many 9V "squared" pack I disassembled had 6 cells inside, BUT there are no guarrantees of what type/size/format. I mean ALKALINE batteries.
Once I oppened an already discharged 9Volts Ever(r)eady batt and I found 6 LR44-type cells, no brand. Four of them were stacked and the other two were lined with the stack. They perfectl;y fit in the 9V box. So, I bought a fresh, new 9V Eveready, externally the same type and oppened it. I found 6 thin batteries, one aside the other, as six sticks. I could not use them anywhere but in some experiences. Later, in another same Eveready-type, I found six bar-type, squared stacked cells. This one had no specific case for each cell, it was really a stack-type battery. Three different arrangement, three different cell types, same brand.
I do not know about the rechargeable ones (is yours a NiCad or an NiMH?), but I am "almost" sure there will be six cells, serial connection, ~1.5 (or ~1.28) volts each. About size and shape, I have no guess.
Success. And tell us about it, please!!!
Cheers.