Role hirarchy is necessary to delete the record with "Delete" permission on profile / permission set + "Read/write" as OWD on that object.

If you don't want role hiererchy enabled for that object then you should have OWD "Read/Write" + "Modify All data" permission

Role hirarchy is necessary to delete the record with "Delete" permission on profile / permission set + "Read/write" as OWD on that object.

If you don't want role hiererchy enabled for that object then you should have OWD "Read/Write" + "Modify All data" permission

If you want to give the permission through permission set then

1. create a custom permission and set the value to true in your existing permission set.
2. Create a custom button with Apes + VF/Lightning
3. In Apex code if the current user has that permission set assigned if so delete the record through apex.