I have plenty of spares on the shelf in storage, thus I would have.
It is unclear to me if you cut off that one strand at the head, or mid way.
There have been times that I tried to avoid changing one, but I found that if I left one strand cut part way, I ran the risk that the one strand would be trouble later, it often was. I think it best to cut off that one broken strand at the head so part of it cannot unwrap inside the outer housing, creating a snag.
Expendables, like cables and chains, cassettes, Rohloff sprocket, brake pads, Rohloff oil, I keep spares on the shelf. I try to stock up only when on a good price but occasionally have to pay full price.
I usually wrap cables with tape before I cut them, that reduces chance that I will end up with a squished mess. Dan has taught me to dip the ends of cables in Superglue to glue the strands together. I do not know how long you have to let the cable sit before touching it to anything after teh Superglue application, I have used 15 min for the glue to harden which might be much longer than necessary.