Minecraft: 1.12.2
Forge: 14.23.5.2847

Mods: 2 to 3
cyberware-1.12.2-0.2.11.21
jei_1.12.2-4.15.0.291
ReWIRED-1.0.7

There are some Cyberware Parts that need certain other parts before you can install them... however you can get around. Here's how to do that with the Fall Bracers.

Fall Bracers with no Cyberlegs.
First, install any Cyberleg, doesn't matter which one... then remove the Cyberleg while re-attaching your Human Leg and you'll notice the Fall Bracers are removed... however if you click the empty space where the Fall bracers were at... they will re-appear, now perform the surgery and open up the Robo Surgeon's GUI and you'll see the Fall Bracers are still installed despite not having any Cyberlegs. The Bracers function without any drawbacks.

Here is an image showing some of the Cyberware Parts being installed without needing any Cyberware Arms/Legs.

Some of them function while others don't appear to do anything at all with no Cyber arms/legs. Here's a list alongside some info about them.

Linear Actuators
You won't jump higher & also unable to launch yourself via Shift-Jump unless you have Cyberlegs.

Aquatic Propulsion System
Doesn't appear to do anything at all in the water with no Cyberlegs.

Retractable Claws
No damage boost for unarmed attacks but it also appears that even with Cyberarms installed you still don't get the damage boost for unarmed attacks.

Reinforced Fist
Can't mine stone if unarmed with no Cyberarms.

Quickdraw Flywheels
Bow Drawspeed is indeed increased without needing Cyberarms. The Drawspeed only applies to Vanilla Bows by the looks of it so if using Tinker's Bows/Crossbows for example... the boost won't apply.

Fine Manipulators
Can't perform 3x3 Crafting without Cyberarms.

If going with ReWIRED parts...

Plasteel Fist
Can't mine at iron-level as intended with no Cyberarms.

Projected Kinetic Barrier
You are able to reflect projectiles back without needing Cyberarms.

It may be possible that I might've missed some but the above ones is all I found so far. Tolerance is still taken if having them installed despite some of them not functioning as you need Cyber arms/legs for them to work but some do slip by.

The Retractable Claws may be bugged regardless as without them I deal 1 damage on a Cow and with them... still 1 damage.

Quickdraw Flywheels unsure if intended to not work with Tinker's Bows & Crossbows. Have to check if other modded bows also apply.

Just curious if this was looked into, seeing as it's an exploit bug of some sorts.

There's no easy way to remove cyberparts with missing dependencies. Also, this may still happen upon death with partial removals. Long story short, the only way to handle this is to maintain the essence cost but disable the functionality.

Fall bracers has the issue.

Claws needs to be enabled/out with an empty main hand to have any effect. Also, you only require cyberarm for your main hand side.

Claws are increasing speed instead of damages, also, in some case, they also apply to armed combat too. This is fixed in next update.

Fall bracers only protect from minor fall damage which is why I left it possible to use them without cyberleg. The actual problem being we can't have a dependency on jump booster not applying to fall bracers. That being said, I think fall bracers are better suited to always prevent fall damage, it'll make them more useful and less confusing. This is part of the next update.