As long as you create a 301 redirect which works correctly, and it still links to related content which is similar to before, it shouldn't be an issue in the long run.
However, you may notice a slight dip when you first make the changes, whilst the search engines adjust and re-add your new, correct URLs.
As long as you can avoid 404 errors (page not found) from happening at any time, that should reduce the risk massively. It's when a page changes and a good link goes to a 404 that you will run into ranking issues.
The same rule applies with the images. If someone clicks an image on Google images, and it goes to the wrong URL and lands on a 404 page, it could lose it's ranking. I can see the new platform uses Wordpress going by the wp-uploads/ path, so you might be able to rely on a plugin to ensure this doesn't happen, such as a redirection plugin.