Combining Batteries (Doing it safe)

[Corrosion.]

I have an old set of computer speakers, I ripped out the circuity and added some 3.5mm jacks for input/output and made a cheap cardboard box speakers out of a $20 wallmart sub woofer so I can take the thing to school easily.

heres my problem.

The amp (computer speaker circuity) is in a radioshack enclosure running on two 9volt batteries wired in a series

If I need to change the batteries I have to take the damn thing apart to put new ones it :/ This could get annoying.

So.. I have 2 batteries form this

each one is 6v 600mAh

So together its 12v 1200mAh (if wired in series)

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If I charge the one of the two batteries will it charge the other in the series? or is this dangerous? If so should I include a switch to disconnect the two batteries from each other before I charge and then charge the two separately.

And if it is safe seeing as one battery takes 2 hours to charge then total charge time in sequence is 4 hours correct?

A few more questions

Is it safe this way

Is it safe to solder on the batteries contacts

Is 1200mAh more power than two 9volts?

Thanks guys

EDIT

Will I need a better charger to do this? seeing as the voltage has doubled?

EDIT

Ok guys heres what you do if anyone else need this...

When wired in series as shown in the image at top of thread the voltage will increase ex: two 6v in series = 12v but your mAh will not increase so in this case the two batteries are 600mAh a pecice and will not increase when in a series. You will need a better charger than the one used for a single battery.

I'm buying this for it. http://www.hangar-9.com/Products/Default.aspx?ProdID=HAN103 Technically a 15v 600mAh would be best but this'll do just fine