You are right that your normal Dry cells and Alkaline batteries are advertised as 1.5v compared to NiMH / NiCD rechargeable that give an output of 1.2v but you should be able to use most of your devices that are advertised to work with 1.5v batteries should work perfectly fine with rechargeable NiCD / NiMH batteries that give 1.2v because the important thing to note regarding the voltage of a battery is the voltage output  a battery provides to your device when it’s under load.

Alkaline battery have a voltage of around 1.5 – 1.6v off the shelf, but alkaline batteries have a sloped discharge curve, their voltage drops over the life time of the battery until the battery is not usable, hence an  voltage of a alkaline battery quickly drops to around 1.25v under actual load, and around 1v when its almost discharged, also alkaline batteries suffer from high internal resistance thus they are not ideal for high drain devices, whereas an rechargeable NiMH battery voltage is around 1.35 – 1.38v when its fully charged and under load it starts around 1.25v and then stays around 1.2v and continues to provide 1.2v until the battery is almost fully depleted, normally the voltage provide by an rechargeable NiMH battery is much more constant when you compared it with an voltage output of an alkaline battery.

The only problem you can face with NiMH rechargeable batteries is that if you have a device which requires 4 or more cells in series then it can create a voltage drop due to the low voltage of NiCD / NiMH rechargeable batteries and the device might refuse to run or power on, but I have found only a handful of devices which behave in such a manner, almost 90% of the devices I have tested work fine with NiMH batteries which provide 1.2 volts.

Most new electronic gear / equipment manufacturer’s take into account the lower voltage of rechargeable batteries hence you should not have any problems with the same, if some of your devices do have problem with NiCD / NiMH rechargeable batteries of 1.2v and refuse to work due to low voltage you can try out the new NiZn rechargeable (nickle Zinc) batteries which give a voltage of 1.6 volts.