That seems worse to me. Sometimes you can gain some info by just the hostname, and pages in the URL. Now all you'll see is random numbers.
And are you really going to spend the money to check every url you have ever published? You have to do it by hand you know. A tool can help but won't tell you if the content of the page changed.
If you want to do this properly use global footnote numbering in each issue. Publish the real URL and the page title (very important since you can google for those words). Each url gets a footnote number that is unique in that issue and you print the number near the url.
Readers can lookup a url by the magazine issue and footnote number.