It plays a LOT differently with melee.

The cyberpsycho missions are meant to be non-lethal. You are not supposed to kill them at all!

I use any blunt weapon to take them down, but you can also sneak up on them (most of them anyway) and do a non-lethal takedown.

You can use pistols to take them down non-lethally, but that's best done with the Cyberpsycho HP bar visible (option in the game settings) and shoot them in the legs down to about 3 % health and let them bleed out. I recommend pistols with Chemical damage for this.

Top tip: use the Optical Camo cyberware to sneak up on enemies more easily (applied to middle mouse button - will replace grenade slot). The Epic (Purple) variant can be purchased from the Ripperdoc at Kabuki Market.