Redesigned website SEO concern

So the story goes like this.
I have redesigned a wordpress site for a client that has some 30+ pages in Xara. The SEO is about done and soon the site will replace the wordpress site.
The old site will be deleted and the new site with Xara will be uploaded in its place.

My concern would be the following:

1) The old site has over a hundred pages, most were named and not used, somehow those 100 odd pages still linger in google and are indexed and the previous designer did not redirect them with error.

An example can be seen as such, see link below, not sure what the web designer had in mind, ignorance or lack or know how or just did not care to delete them from wordpress.

LINK

My question would be, when I delete wordpress and start with a blank sleight and upload the site done with xara, do I have to worry about those dead links from the previous site?
When will they be removed from Google?

Thank you in advance.

It will be a mixture of add a set of redirects to the WP .htaccess file, delete the pages other than a "We have moved" that no one need ever see.
The dead links will have fallen off Google last by now as few will have visited them. Have you evidence of any Google Search finding them?

Google will update in its own sweet time unless the OD set up Google webmaster visibility. If so, you may be able force things along.

Acorn

You can go under the search-console @ search.google.com if you have this site listed as one of your sites. There is a removal section to tell google to disregard old links.

I had some issues earlier this year where Google was notifying me about some problems with my site and it keep showing all these old links. It took awhile to enter them all but slowly Google removed them from their listing.

Ray

Thank you Ray. Once I upload the new site, I will get the code from search-console to install in Xara and register it. Yes I have done the remove old links before but it takes forever. I may wait a bit to see if google takes them off without my assistance.