The secret is that Finder's preferences will show or hide actual volumes, i.e. any item that appears in OS X's /Volumes folder: partitions, iPods, CDs, DVDs, etc. But it doesn't control the display of aliases. So here's what you do.
- Show all hard drives. Open Finder -> Preferences. Select the General pane and check "Hard disks".
- Create aliases. Select a hard drive you want to keep on your Desktop. Control-click (or right-click) the drive and choose Make Alias from the contextual pop-up. Finder creates an alias file for the drive. Repeat for each drive you want to keep.
- Hide the drives. Return to Finder -> Preferences and uncheck "Hard disks". Your hard drive icons go away but the aliases remain.
- Rename the alias. If desired, return to the Desktop and rename each alias so it looks more like the original item. The arrow that appears at the bottom left of the drive icon indicates that you're dealing with aliases and not the original drive.
Be aware that View -> Arrange By does not treat aliases as drives, so your disk may end up in an unexpected position after arranging.
Thanks everyone who suggested aliases.