We see a very similar piece of tech in The Dark Knight. It is, apparently, powered by a 'device'. There's no indication what the power source is, but a taser doesn't need to have a big battery to be highly effective, probably there's a small rechargable battery built into one of the ears of his cowl that also powers the voice modulator and other gizmos built into the suit.
Over time the cowl's wiretapping capabilities were upgraded from short to long range. We also improved security. Originally four-part hidden snaps were used to protect my identity should I be knocked unconscious. I have since developed a device intended to produce an electrical shock, activated if anyone tried to remove the cowl externally.
The Dark Knight Manual: Tools, Weapons, Vehicles & Documents from the Batcave
Another similar piece of technology appeared post-Crisis, wired into the batsuit and explicitly labelled as a "taser". It's normally used as a melee weapon, but also defends the cowl. It's sewn into the suit, evidently along with the power source.
ALL WIRED UP
A “last resort” taser system is sewn into the outer layer of the Bat-suit atop an insulated internal lining. This one-shot defensive mechanism shocks up to 200,000 volts through a micro-thin electrode network dispersal over the entirety of Batmans costume. The taser is armed and fired via circuit-wafer controls in his gloves.
Batman: Visual Dictionary
Since Alfred has direct knowledge of the suit, disabling the taser or removing the suit without triggering it would just be a case of not putting your hands onto the dangerous bits.