The first thing is: this is a rather surprising change: you are going from a very good URL structure ("/news-and-results/middle-districts-2019.html") to a fairly bad one:"/107-results-2019/314-middle-districts-friday-17th-may-2019"
If you are redoing the site, I would strongly advise:
1 - do not include /index.php/ in your URLs. That's a one line change in your .htaccess and one setting in Joomla. In 2019, just do not do that.
2 - You now use item ids in the URLs (ie 107-results-2019 instead of just results-2019). That's also not very good. Not so much for SEO but mostly for practical reasons: when you move/redo your site again, your content will have different ids and it's next to impossible to do redirects because of that.
Now about your question:
1 - The "problem" will not be the same with sh404SEF because sh404SEF will likely NOT create URLs such as /results/107-results-2019/314-middle-districts-friday-17th-may-2019. It can be set to include ids but it normally does not. Also, it will not use menu items to create URLs, as you may do, but URLs will only be created based on categories and item titles.
2 - As for the redirect, we do have a strong redirect engine so you can certainly redirect any URL you want to a new one. You can set these redirect one by one (ie tell sh404SEF to redirect /news-and-results/middle-districts-2019.html to /results/107-results-2019/314-middle-districts-friday-17th-may-2019) or you may be able to creat redirect "rules" where many redirects are done with just one command.
I doubt however you can use "rules" as the article titles are different and you included item ids in URLs. But you certainly can do those redirects manually in sh404SEF.