There are couple of approaches that you can try.
1. Hide the element
Use Chrome inspector to find the exact class/ID for the 'Delete' versions link and then hide it using CSS. You need to add this CSS to all the pages (probably adding it to a master page will be a good idea). You will also have to take care of 'Delete All Versions' link.
2. Override JS function
From Chrome inspector I can see that 'Delete' versions link calls JS function DeleteVersion
. You can override it by using below sample code.
var oldDeleteVersion = DeleteVersion;
function DeleteVersion() {
alert("Deleting versions is not allowed.");
}
Again, you need to add this JS to all the pages (probably adding it to a master page will be a good idea). You will also have to take care of 'Delete All Versions' link.
Also, may I ask why you cannot modify existing permissions? That will not only be the easiest, but also the recommended option. The options that I have suggested will require you to thoroughly test as you are overriding what is provided by SharePoint.