I am not sure I understand your questions.

I assume the Energizer Ultimate is a Lithium battery.

I am going to assume "Slow to take a picture" is either flash recharge time or shutter lag.

I am going to assume "recharge the camera" means recharge the flash.

A different battery will not help flash recharge time, however a new or fresh battery will recharge the flash a bit quicker.
Flash recharge time is usually about 2 to 3 seconds on just about any camera.
It depends upon how far the subject is from the camera.

Shutter lag is the time from when you press the shutter button until the picture is captured.
It is mostly caused by the time it takes to auto focus.
A different battery will not improve this.
You can press the shutter button half-way down then re-frame the shot and then press the shutter button the rest of the way down.
By the time you do all that, the camera has had time to auto-focus and the capture time is less than 0.1 second.