Is there a way to do this? The fixer doesn't seem to like it when I kill them.

In the early game baseball bats are your friend. :)

mod lethal weapons to non-lethal is one option

other is use melee for the last couple percentage points of psycho health

or get a chemical damage / poison damage gun

and let the last few points drain as you get there

im sure theres more ways

personally, i couldn't stop laughing for most of my cyberpsycho rampage - after hail of bullets and all sorts, id sort out the final percentage points with my trusty power dildo

worth mentioning, when taking stealth dudes down, dont kill, do non-lethal, then beat their heads in with dildo after, helps your....dildo hand experience ;D

enjoy

Use blunt weapons or get a non-lethal mod, either for your guns or your cyberware optics (but I'm unsure if the mods work properly everytime or if they're a bit buggy in the games current state).

Takedowns can also be non-lethal, but are not really an option on the cyberpsychos.

Edit: Oh, and hacking! You can hack them with non-lethal mods.

You can also do it with the "system reset" and "short circuit" hacks if you've invested enough skill points into quickhacking. System Reset is the best one, if you have the RAM to use it, because it knocks the target unconscious even if they're at full health, so you can remain hidden and not even have to engage them in combat. It works on bosses too.

I've found repeatedly shooting them with lethal guns works for some strange reason. (Yeah... a Nekomata sniper rifle to the head a few times and they still keep breathing after they go down. I can shoot them again and get bonus street cred + cash too)

Wrist launcher with tranquiliser ammo. One shots them every time.