Before going into the mechanics in detail:
You might have noticed that Electric Damage is very lethal in nWoD.
It is also broadly speaking inaccurate, but that is ok.
In nWoD Damage is related almost solely to voltage, in reality current takes a more important effect. A Shock Baton or Electric Fence is actual high voltage, low current.
So is kinda more dangerous in WoD than in real life, maybe. That doesn't really matter.
Perhaps in the this dark mirror of the world, protective fences were made to harm animal brushing against them, rather than merely scare them.
Remember you God Kills a Kitten every time you try and introduce real world physics into a RPG. So don't get too distressed.
Ok, for a start I just want to make sure you have the damage mechanics for electric shock correct.
Electric shocks deal flat damage, no rolled damage. (Page 178, top of left column)
Electrocution automatically causes bashing damage per turn of
exposure. No attack roll is made.
So assuming you just took someone and held them up to an electric fence, they would take 6B every turn, no roll made.
Now hitting someone with a baton is going to hurt, electrified or not.
Just like hitting someone with a touch that is on fire will leave bruises and burns.
So extending all this, the logical progression is:
Do bashing damage equal to:
Strength + Weaponry + 3 (baton) - Defense - armour*.
if you get at least 1 success, then deal an additional 6 Bashing damage.
Now automatic damage like this is a thing in WoD. it is normally reserved for explosives.
For example a Stun Grenade is
1B+2 automatic (page 104 of armoury).
But look at those numbers, clearly
3B+6 automatic is completely unreasonable.
*Technically things get weird here, because armour doesn't apply against electric shock,
I suggest allowing it in this case, cos otherwise things are too confusing.
Automatic Damage Level
I think asserting a stun baton packs as much punch as a Electric Fence is a bit excessive. Bearing in mind sticking a fork into a toaster is only 3 Bashing, no one (except a PC) is going to make a weapon that is worse than sticking a fork in a toaster. That is not a "less harmful alternative to shooting them"
It could also be argued that when hitting someone it doesn't get held for a full turn.
So perhaps it should be an additional 2 or 3 bashing damage.
If it is packing a full 6 Bashing each turn I would say battery life at least should be a concern, eg. 3 shots before it is flat.
I would also say any weapon of this type (doing automatic damage) is illegal, and police would confiscate it, probably with just a stern warning unless it was used in a crime.
Compare similar weapons
These all present Options you and your GM can work with.
Stun Baton (Armoury)
Beyond the actual Stun Baton rules in OpaCitiZen's Answer.
I recommend reading (and upvoting) his answer.
It is the correct solution for using something that is standard.
There are the other similar weapons with rules presented in WoD books.
Which you and your GM might like to use to guide you in making rules for such a weapon.
Range Stun Gun (Armoury)
Ranged Stun Gun is a thing: on page 93 of Armoury.
The mechanics on that is basically (paraphrasing)
Shoot at them with Dex + firearms -1 (weapon penalty)
If get any successes they take exactly 1B damage, no more, no less
Each turn after may press the taser trigger to deal a automatic 3B
Removing is difficult
Stun Gun (Hunter)
Hunter on page 248 present the same weapon, but with the modification:
Once damage accumulated exceed targets size, they become unconscious
Hunter also presents a Held held Taser (not ranged) page 248:
Handheld Taser/stun gun: Has a similar effect [to range stun gun], except
that the user makes a Dexterity + Weaponry roll to hit the target. No
damage is inﬂicted, but successes count toward the knockout effect
mentioned above. The user must make successive Dexterity + Weaponry
rolls to continue applying the electricity; successes on each round
are subtracted from the target’s efforts to break away (Strength +
Brawl, one success ends the attack).
This is pretty weird as it has a hidden damage pool that doesn't count.
and need to be tracked.
I wouldn't use it.
I would like to present One more option
Ok, it is a Stun Baton, so it stuns people, that makes sense right?
The stun effect is a thing:
If the damage caused by the attack meets or exceeds the target’s
Size, the target loses his next action.
Lets make the Weapon bonus is
+5B (instead of
+3B) to represent the extra shocking, with the Stun effect.
So if you do damage exceeding their Size (ie for most people get a exceptional success will do it), they are Stunned.
I would lean towards using this, purely cos it is simple.