No, you would not need a fuse for that. The converter will have a current limit built in, so the fuse would only be protecting the red and black cables, which are not long enough to be worth bothering with a fuse. Make sure the cables are not left loose so that insulation can get damaged, use some cable (zip) ties to keep everything secure.
You could use a Viofo hardwire kit instead of that converter, and you could use a fuse tap to connect it to the fuse box instead of intercepting the lighter socket wires. That would be more normal, but maybe you have good reasons.