I saw the stun baton on Meridian's LP, and much like him (and Eddie) thought it wasn't very interesting, although it has potential by being a fast, small stunrod and the idea of electric stun weapons with fixed damage makes sense as it is the shock that does the stunning rather than brute strength. Maybe it could scale to some extent with melee accuracy? We've talked about weapons that don't scale and how they are inherently unfavoured before, unless they are overpowered to begin with (the rod being close to that, being balanced because of the stun bug and the high TU cost).
Looking at the stats:
Weapon Accuracy TU Cost Damage
Handle: 0.7*(0.34M + 65) 9 10 + 0.2S + 0.4B
Fistycuffs: 0.65M 8 0 + 0.6S + 0.2M
Cattle Prod: 1.1M 20 70
Stun Baton: 0.8*(0.5M + 50) 8 30
(For simplicity, I'll consider 2 hits of all the 8-9 TU cost weapon for every 1 hit of the cattle prod)
So the champion in scaling is obviously the fistycuffs, and it will always have a place on the melee monsters. It also has bonus damage to health which may help stun by reducing HP, but also kill weak targets (I have started to bring handles for my melee monsters to stun weak targets like GOs and academicians). At a reasonable 30S and 70M you get 32 damage to equal the baton (but less accuracy; the Stun Baton always leads for accuracy). At a similar 80M and 32S, you get 35 damage and match the cattle prod in stun per TUs, although that assumes 0 armor for the target and your accuracy is once more much lower. Boost the stats and the fistycuffs start taking the lead against lower armor values. With a maximum damage of 76, it is possible for a monster (gal at the stat caps) to get better damage out of the fistycuffs. Fistycuffs take 111 melee to beat the handle in accuracy, but their damage scales very differently so it strongly depends on the gal. At 25S, both do 15 damage + their other stat bonus, so it becomes a choice of do you have melee accuracy twice as high as your bravery? And you better have good melee for the fistycuffs otherwise the handle will hit more and be better any ways.
For the handle, with 40 Bravery (the average for a swabbie 10 min, 70 max = 40 avg), you get 10+16 = 26 damage, so you need 20S for the extra 4 damage and the handle is already as good as the Stun Baton. The 1 TU difference doesn't matter much, especially since it is easy to improve on the S to get a few points of extra damage. The handle has better accuracy up to M=34. Plus the gals enjoy handlin' other people! It is definitely the best starting weapon for brave gals. At the cap, with 100B and 80S, you can get 66 damage out of the handle and being twice as fast as a cattle prod (plus easy to carry on the belt or QD slot) it is then better in almost all cases. At a more realistic 70B and 40S, you get 10+8+28=46 damage, which is better stun/hit than a cattle prod on enemies with less than less than 22 armor (at 22, they are equal 2x(46-22)=48 for the handle; 1x48 for the cattle prod). Accuracy suffers above M=49 for the handle though, and it will miss more often than the cattle prod.
In view of this, the Stun Baton is not as bad as the numbers look. It beats the handle for cowardly gals (at 10 bravery, even with 80 S you only do the same 30 damage the baton would do). It is also more accurate from M=34 onwards, so it definitely has an edge for gals with good melee but low bravery. Under M=53, the baton also hits more often than the stun rod, so for gals that are terrible at melee and cowardly (otherwise the handle is better), it is the best stun weapon. However, the handle is at most 25% less accurate than the baton (and generally less so), so as long as you can do 38 damage with it, it is better than the Baton at Acc*Dmg/hit. For the Baton vs Fistycuffs: past 70 melee accuracy, as long as you can do 45 damage with fistycuffs (so 50S), the Fistycuffs are better at Acc*Dmg/hit. These are not difficult numbers to get.
I would suggest scaling electric weapons weakly with melee accuracy. Especially for the stun rod since it gets no scaling past 80 melee accuracy (already 100% to hit, discounting melee dodge). Scaling (representing zapping of vulnerable areas: head or armor weakpoints?) by 0.1 would be enough to give them a bit more edge. This would make the stun baton better than other weapons for cowardly and weak gals (the handle is really good if you have high bravery, the fistycuffs get great at high strength and that's an easy stat to cap) and further establishes the stun rod as the meanest early-tech melee stunner since it is otherwise rather easy to surpass in stun/hits (this would also help the Baton to approach the Cattle Prod in Acc*Dmg/hit).