Flows that are Shared to SharePoint List requires Users to have at least Contribute permissions

I have a Flow that is manually triggered by pressing a custom button inside a SharePoint Document Library.

To allow other users to manually trigger the Flow using the button, I have shared the Flow with the SharePoint List as below:

This works well as I don't have to share out the Flow to each and every individual who needs to use the Flow. However, I have found that the user requires at least Contribute permissions on the SharePoint Library to be able to use the Flow.

I attempted to create an Permission Level without the "Add, Edit and Delete Items" List Permissions unchecked but this breaks the user's ability to run the Flow.

I want the user to be able to run the Flow but not be able to modify anything in that Library.