You are correct.
When swapping batteries between two equipment provider, these are the factor that you want to take a look at:
- The voltage
- The capacity
- The form factor
- The battery chemistry
Voltage is important for your system. It expect a certain range of voltage. Capacity is flexible, but if it is smaller, it will reduce your cycle time in between charges. The form factor will allow the battery to fit correctly on your device. Last but not least, the battery chemistry is important for safety and charging purpose.
In your case, you have two AA battery in series : 2.4v and 2.4 for your proposed replacement. You have also a capacity of 1300 mAh for both products. The chemistry is the same (Ni-MH) and the form factor is the same.
It should therefore work without any problems.