Battery choice for powering 3 servos

Hello,

My project is going to be a simply airbrake device for model rocket.
A BMP280 will read the altitude and trigger the three servos to pull open three flaps when it reached a preset altitude threshold.

I read from other posts to learn that I shouldn't power the servos through my Arduino nano and that the servos are operational at 4.8-6V. I also read that a single servo usually draws around 500 to 700 ma when it operates, and only a few ma when it's idled.
I powered it with a 4.8V NiMH 2000mah battery during experiment, and the servos seemed to function just fine. The problem is that the battery is quite heavy for the rocket and I would love to cut weight...

I am exploring options to cut weight and came across a 4.8 NiMH 220mah battery on Amazon during research, which seemed to be much lighter than my 2000mah battery.

Since I only need to supply enough power to the servos to operate for a few seconds and maybe several minutes of standby time before launching it. Three servos will operate at somewhere between 1500-2100 ma, and a 220mah battery should be able to operate the three servos for around 6 mins and idle for hours, which maybe all I need.

I wonder if my assumption is correct and can move forth to get and use the smaller battery.
Any advice or explanation would be appreciate.
Thanks!

Rockets are so weight sensitive. Batteries, always heavy. As are three servos. So, why not use a spring operated mechanism instead, as it will only deploy once in flight? You could use a small solenoid or electromagnet latch to release the spring.

Consider a low voltage, lightweight (12 gm) solenoid, like this one: Mini Push-Pull Solenoid - 5V : ID 2776 : $4.95 : Adafruit Industries, Unique & fun DIY electronics and kits

Much smaller ones can be found -- these ones weigh only 1.6 gm

You can also reduce the current requirement of the solenoid by driving it from a decent sized capacitor. It will supply the transient current that the solenoid needs, without requiring a huge battery, as would be needed to hold the solenoid in an active position (which you really don't need to do). Just keep the cap charged through a resistor. Caps tend to weigh less than batteries.