I would guess that Arturia has nothing to do with Abletons presets.
So i would think you shall back-up your Ableton presets and move them to the new disk.
And then i guess you have to be sure, that the paths you use in your Ableton presets to open Arturias applications with the Ableton presets, is the same as in the old one, or be sure you can change the paths very easy.
In this i pressume thats how Abletons presets work. I don't think you can open a Ableton preset inside a Arturia application. I don't think a DAW preset save the Arturia (or any other applications) preset it self, but only a path and the settings for an application/ the application and alike.
If the Ableton preset had all data and functionality, then you could use it without having the original third party applications, i suppose. So i don't think this is the case.
Actually i would allways save my presets as a Arturia preset and back them up too, so they are availble inside Arturias applications to use anywhere. And then save as a Ableton/ a DAW preset alongside when needed.
Hope this helps you.
I don't use Ableton. Perhaps someone who use Ableton can tell more.
But i think i would do the above anyway, to be sure to get things to work as easy as possible.
I can also suggest you ask in Ableton forum. As i see it, this is about Ableton.