Will hacking off old blown render damage internal walls

I want to get a new kitchen but I also want to get the rear of my house re-rendered.
While getting quotes about the rendering they mentioned the old blown render would have to be hacked off, the sound stuff could stay. Some sections do sound hollow at the lowest parts of the walls.

My kitchen and bathroom are currently being dot and dabbed and skimmed but I'm worried that if I fit my new kitchen now, will the rendering damage my internal walls/plaster to crack? Should I delay my kitchen...

Will hacking off old blown render damage internal walls