Here are steps for you:
1.Go to site settings, activate SharePoint Server Enterprise features both in site features and site collection features.
2.Go to site permissions -> permission level -> view only -> copy permission level -> give a name to the new permission level, like "Edit without Download" -> Enable "Add Items" and "Edit Items" check boxes under "List Permissions".
3.Grant other users with "Edit without Download" permission level for the excel file.
Result of users with "Edit without Download" permission level, without Download option.
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