Purely kinematic objects - How to disable physics completely for specific parts?

I want some objects to not interact with the world in any physical sense, but at the same time, I want to be able to use scripts to control them. This is a very common feature in game engines, necessary for all sorts of kinematic effects, such as (in my case): floating pick-ups, which have a custom floating animation, but don't interact with the world unless being touched by the player.

Trying to disable CanCollide while anchoring should in theory do the trick, but for some reason this creates terrible physics glitches when trying to interact with the object. This is also mentioned in this Tools tutorial:

Make sure all of the parts are not anchored when you are finished building. If any part of the Tool is anchored, the Tool won’t be able to move and the character will get stuck when picking it up.

Is there any chance to achieve purely kinematic objects that do not physically interact with the world (except some special circumstances such as players touching)? Ideally I would like this to work with normal Parts, as I want to create custom pick-ups from existing world objects, such as this miniaturized soldier:

!Screenshot

Any help is appreciated! :)