I really didn't like the original handlebar wrap so that had to go.
I had a spare set of cork grips from a previous "Townie" conversion I built up a while back. I decided to change the handlebars on that bike during the build and ordered a second set of cork grips at that time. Glad I did so!
The townie had these handebars:
after a few rides, I didn't like the flat bars and swapped them out for these: (the VO porteur bars)
The second set of cork grips came in very handy. I also had some left over cloth bar wrap as well as some nice leather twine and got kind of fancy on the handlebars: