What is the default cursor icon for delete?

There isn't one but you can create your own icon and use cursor: url(); CSS to accomplish this.

More info here: https://developer.mozilla.org/en-US/docs/Web/CSS/CSS_User_Interface/Using_URL_values_for_the_cursor_property

Example:

div {
  cursor: url("https://i.stack.imgur.com/bUGV0.png"), auto;
}

<div>Hover Here</div>

not-allowed is the only one that makes sense, however the custom jpg url option looks pretty simple.

You could also rethink your UI design to get around this. You could just stick with the intuitive default behavior of a checkbox, and let the user click it with the understanding that the checkmark will toggle. No fancy control key, no fancy cursors. Maybe just a pointer icon in either case. With some separate add / remove action buttons.

You could also think about showing some clickable icons for add / remove (per item if applicable). Thus not using a checkbox.