I would put black linen on the cue.
Here is why;
1.) The cue is very busy on top and bottom, and IMO, THAT should be focus of the cue.
2.) I have seen many cues that have a lot of inlays and then put a "busy" wrap on it, and it makes it look "over the top" or "gawdy" .
3.) I think if the cue was plain jane, or simple 4 point with no inlays, I could see adding the wrap.
4.) Nice cue either way, JMO.
Ken
PS Looking at the music cue on your signature line, shows exactly what I am talking about. The plainer looking wrap, doesn't draw your attention away from the music inlays. A "busy" wrap on that cue would be a mistake too, IMO.