If you go to the store and by a 9v alkaline square battery and test it with a volt metre, it will read about 9.6v when it full and it will drop to about 8.6v before its officially dead. Same with an aa at 1.5v it will read from 1.65 full to 1.4 empty.
Alkalines start over there rating, and drop off as they waste. Ni-cad Ni-MH, put out consistent voltage pretty much from full till empty. So anything that says it takes alkaline batteries will be fine with a few percentage above spec. If the weren't then duracell and energiser would have been in a lot of trouble by now.
So your rechargables in series wiring are putting out close to what an near empty set of alakalines would in terms of voltage, but they are consistant until they die. The alaklines start great and get worse (recycle time gets longer) This is also why a lot of devices when presented with rechargable batteries indicate half or low power because they measure voltage on the assumption that it will fall as the batteries waste (not true for the rechargable variety, well true to a much lesser degree that they can't measure)
If it was mine I'd happily take the 9.6v, but as its your flash and I don't want to bust it on you, I'll say go with the 8.4v, your flash will see that as a slightly used battery. That battery is likely to have a slightly higher output in terms of mAmp/hour (how long it will last) and if you don't want to change batteries thats all important
I have taken appart a rechargable 8.4v from an airsoft gun and it was pretty much 7x 1.2v AA rechargable cells in series stuck together in another package. It was in a 3 down, 3 up, with a squashed 1 joining the 2 sides. I was going to use some of the 9v alkaline variety to replace this but they turn out to be around 1100 mAh output so they would last half as long as 6x1.5v AAs at 2200 mAh. The I was going to use 2x9v in parrell wiring so still 9v but now with double capacity of 2200 mAh, but then I lost interest in the whole thing.
So in summary an RC 8.4 should be fine, and a 9.6 should also be fine, but likely no extra benefit and it will drain faster. But nobody knows for certain how your flash was built so if it or you get blown up its your own fault.