I wrap my wire in 1” (2.5 cm) wide floral tape when I want that extra protection on a deciduous branch. I wrap it at an overlapping 45 degree angle keeping constant tension while wrapping. I don’t wrap the tape around the wire; instead, I turn the wire between my fingers while pulling it away from the tape as it unspools. Because floral tape sticks to itself, this whole process doesn’t take long and the paper stays in place if you wrap it enough tension.
I bought light green tape thinking that it would be less noticeable. In hindsight, I want it to be noticeable so I can see at a glance that the tree is wired. When it blends in it’s easy to overlook a branch and, even though wrapped in paper, wire damage may occur on soft bark if you didn’t check a tree in time. Next time I buy some tape it’ll be a bright, contrasting color. You can buy the 1” tape on the internet. It comes in several colors.
Here’s an example on a short piece of wire:
