Thank you all for your helpful comments.
I think I will go with the solution building the new site in a sub-directory.
The old site is quite large (100+ pages), and therefore I plan to merge some content from the new processwire-subdirectory via the fantastic API that processwire provides into the old site, during the conversion-process. Quite messy, I know. But with such a complex-reducing system as processwire, I think it is doable.
Thanks again!