I *think* you should be ok with the channel set band, but honestly- with an irreplaceable antique setting you love, I would wear a super thin spacer - just for piece of mind.
I think it’s ok with the channel set. I would do it. Unless the band is particularly sharp edged…if you got a spacer it should be rounded I think. Pretty set!
I'll third this, it's exposed diamond that creates the most wear.
You are lucky to have two 'walls' or rails doing the rubbing. It will wear, but at a much slower rate- mostly you'll notice the milgrain degrading on your band as it's the lower profile.
A small rounded 1mm spacer will likely keep that from happening and be unobtrusive visually if you choose, but it's not imperative.
This set you have is beautiful together