Get yourself one of these LM2940 5V LDO Regulators -
http://search.digikey.com/scripts/Dk...M2940CT-5.0-ND
read the datasheet, make sure you get the proper input and output capacitors. they're all available from digikey.
Any load (in this case the TP's internal charging circuit) will pull what current it wants. The 1A spec you see on the wall charger is the MAXIMUM current it can provide.
I would use 4 1.5V AA batteries. They will make 6V in Series. This regulator will drop the 6V to a constant 5V. When using a regulator you will need to have a higher voltage input then the output 5V. The LM2940 is a "Low-Drop Out" or LDO regulator meaning it has the lowest input-output differential requirement - so you can get away with as little as 5.5V as an input to regulate to 5V while pulling up to 1A (theres a chart in the datasheet pg 7 top left). Standard non-LDO regualtors may need as high as 7V input.
Remember this is a linear voltage regulator meaning its not as efficient as say a Switch-Mode regulator (aka DC-DC converter), but it is the easiest to implement. You will be losing P = ((Vin - Vout) * Iout) . - So with (6V in - 5V out) * Ioutmax(1A) - your maximum power dissipation in the regualtor will be 1W assuming the maximum current is being pulled by the TP. Depending on the ambient temperature you may need to get a heatsink - look at the figure on pg 11 top left on the datasheet. TO-220 (the package the regulator comes in) is a standard component package and you can find a heatsink on digikey as well. you could also get the battery holder on digikey too as well...