Some links work, other have 404 errors

Is there any way to ensure that the links in all lists are of type 1 above?

Depending on how they are generated, certain lists of downloads on my site have links of this form

1. https://activites-canines.com/download/32791/

Others have links of this form:

2. https://activites-canines.com/?post_type=dlm_download&p=39867

In the second case, the links give rise to 404 errors.

Is there a way to avoid that?
Or is there any way to ensure that the links in all lists are always of type 1.

Examples of list generation giving rise to the problematic type 2 links:

* https://activites-canines.com/?dlm_download_category=compte-rendu-reunion (for example, when clicking on a category in the “Categories” column on the download monitor management page)

* Ajax Search pro live results, e.g., on this page : https://activites-canines.com/recherche/ (example of search giving rise to problematic links : check only “Chercher dans le titre” and “Téléchargements” and search for text “compte Rendu” – then see results 3,4,5 and beyond)
?
As it stands, the only user-end download lists that have correct type 1 links (other than those generated using shortcodes) appear to be those on a standard search results page, e.g.,
https://activites-canines.com/?s=compte+rendu&asp_active=1&p_asid=12&p_asp_data=1&current_page_id=3372&qtranslate_lang=0&filters_changed=0&filters_initial=1&asp_gen%5B%5D=title&asp_gen%5B%5D=excerpt&customset%5B%5D=dlm_download

This is quite a severe limitation for me.