Hi,
You won't be able to change the characteristics radios into checkboxes. It's not technically possible.
The characteristic/variant concept can't work as multiple selection.
I would recommend instead to create a custom field of the table "item" (business edition) and of the type "checkbox".
The drawback in using custom fields instead of characteristics is that you can have different prices/quantities for different variants of the same product but if you don't need that, then the custom fields are exactly what you need.