Hello,
Looks a nice bit of kit... quite expensive for the functionality though.
I don't know this unit.. but can make an educated guess as to what is "under the hood", so to speak..
The actual controller electronics are probably built around one or more microcontrollers .. this type of electronics is DC powered (eventually!) and so you should be able to easily convert it to run off of any mains supply voltage (either a psu rework or even an inline transformer) ... no major problems there..
External sensors etc. will be powered/controlled/read from the main control box.. also no problem there.
You **may** hit snags at the mains switching stages. These could be as simple as a few mechanical relays.. mains rated electronic relays or some sort of discrete circuitry
... there are many ways to do this, although build cost and circuit design constraints probably means that the design is "optimised" for minimal cost.
Your idea to replace the US style connections with IEC panel mounted sockets is sound.. Cheap and easy to obtain.. I've done just this with a few vintage oscilloscope rebuilds where the original power leads are made of "unobtainium".
What it boils down to is this
The controller electronics would need to have their PSU changed from 110V (with what ever the output is/are... 5v, 9V, 12V.. can't tell without looking at the unit or a circuit) to 240V.
Anything that **switches** mains would have to be rated to UK/EU specs. There is a reasonable chance that they are already.
I would certainly rate your proposal as "doable".. Whether it would be cost effective is a matter of personal choice.
If you have DIY skills have you considered building your own version? Something like a Raspberry Pi, ardunio, mid range PIC (my personal favourite!) or one of the many development boards on the market would certainly be powerful enough... There is plenty of information on the web... many people have done similar projects to this..
Good luck!
Bodge99.