Lethal weapons are much more reliable than non-lethal options, which either are unreliable (cattle prod w\ highly random damage), are actually lethal (ball bat) or require a lot of overhead to be really effective (handle and it's scaling from bravery of all things). And at the start of the game you can't really afford to capture everyone.
Axes are different from fuso swords, but I prefer them for a few reasons:
1. Ax is one-handed;
2. Ax has decent accuracy;
3. Ax has high base damage, scales strongly with strength, and doesn't have +xx% armor;
4. Ax is available from start, I think you get one right at the beginning.
I didn't like cattle prods the few times I used them. There have been times when my gal ran towards the guy, spent remaining TUs swinging her prod... but he just stood unfazed. If not for contingency plans, I'd lose many gals to bad rolls.
As it stands, I gravitate towards handles, they are small, easy to acquire and really, really effective at right hands. They're standard equipment for me, placed in quick draw slot, so everyone can go capturing when opportunity arises.
I don't know how you manage to lose entire squad to two guys, but maybe inability to capture them would be nice cue for you to kill them instead. Killing is safer, too: lots of options to fire over the cover, or just blow up the cover instead.
Well I don't know how to help you with aggressiveness. The only advice I can give you is to be as much careful as you are aggressive. Scout ahead. Take vantage points. Use cover, stand two tiles away from corner, leave your gals enough TUs for one snap shot so they could react. Stay away from sources of light. Go in groups of 2\3\4, so your gals can cover\heal each other. Have various equipment and be ready to face e-v-e-r-y-t-h-i-n-g.
Also, ratmen missions are generally not worth it. Too much risk for a bunch of low-tech equipment and a money purse.