I'd like to empty my Edge history for a specific website without deleting everything ...
I don't think there's a one-click method for doing this, so I can only suggest a couple of things to make the process less cumbersome.
On the page edge://history, use the search box to find the URLs you want to remove.
Press Ctrl-D to add this filtered history page to the favourites bar to allow you to open it with a single click.
Press the Page down key repeatedly to extend the list beyond the default maximum of 150 entries.
Use Ctrl-A to select All the entries shown.
Note that there's a difference of 5 (the recent items) between the results found and the number selected.
Use the Delete button to remove the selected URLs from the list.
It wouldn't be too difficult to automate this, if you're interested in a script solution. History is an SQLite database, so all that is needed is a command like
DELETE * FROM urls WHERE url LIKE '%domain%'
run (with Edge fully closed down) on the database
%LocalAppData%\Microsoft\Edge\User Data\{profile-directory}\History
(Each browser profile has its own data store. If you only have one profile, its directory will be called Default.)
While typing that, I realized that this is another possible solution to your problem. You could create a separate profile solely for your cartographic activities. It's only a couple of clicks (on the profile picture in the toolbar) to switch profiles, so if you discipline yourself to use the new profile only for this and your normal profile for everything else, you could happily use the option on the page edge://settings/clearBrowsingDataOnClose to clear the history at the end of each session. There's no need to sign in to the new profile unless you want to make it easier to sign in to Microsoft sites while using the profile, or you want to sync some data between devices. You can't have more than one profile for a specific Microsoft Account or work account.
PS The 'other site data' you can remove for a specific site on the page edge://settings/siteData doesn't include the browsing history - the list of visited URLs. That would be too simple 😉
PPS If you'd like to suggest that the Edge team look into making it easier to remove selected entries from History, you could post at Microsoft Edge · Community. The Edge team visit the site regularly, and you're able to share a link to your feedback item so others can be persuaded to see and upvote it.