Is there an English word for "the ability to be deleted"?

A usable interface should not require to describe the actual action, because the action itself is obvious from the interface element: a radio button, check box, or any graphical toggle element, so a clear message may look:

Enable delete option: On/Off

The word 'enable' implies toggling.

Example from Oracle Documentation

15.1.2.2.1 Manually Enabling Delete Confirmation

This section describes how to enable Delete Confirmation, or add or edit the custom confirmation message, if you have an existing table.

Another option is to use 'removable':

The element is removable: On/Off

Also a good convention (in console/command line interfaces) is putting a simple question:

Enable deletion? Yes/No

No. Deletability is morphologically fine and understandable in context, but it is not an established term (0 hits in COCA, 0 hits in BNC, 0 hits in OneLook) and you run the risk of sounding comical or helpless.

I can think of no other words that would fit the bill.

But all that is beside the point. The option to be toggled already is labeled or called something, and that is the label you must be using. This is techical documentation, not poetry. Refer to things by their actual names.

Toggle the option "[the actual name of the option]".

If the option is actually called deletability, then go ahead and write "Toggle the option 'deletability'". But if it's not called that, then don't rephrase just for the sake of calling it something it's not called.

You also might turn the property around. "Deletability", while understandable, sounds a bit awkward. However, objects that cannot be deleted are often referred to in the computer sciences as "Protected", so you might consider toggling "Protection" or "Deletion Protection" (or sometimes "Write Protection" for files) on or off instead.

Permission is a common notion used in software world. You can use something like 'Delete Permission', or you can rephrase the sentence to

Toggle the delete permission on the object

or

Toggle permission to delete object