Now, this is with the caveat that we are all here looking at pictures on the internet, on our own monitors, and some of the those pics are taken at different times and locations. SO anything goes...
I quoted that line from my earlier post because those two pictures you just posted certainly are a good example of that warning. In those two pics, the installed materials all look great together. What looked to me to be a grey wall in the first series of pics you posted, now look to be a much better match. I'm seeing many tones of brown and tan, that I didn't see before, that go well with the installed pavers. And both look good with the aqua tile, which compliments all those same tones.
The point is, you can't rely on specific advice about color from the internet. The only thing that matters is what things look like in your yard, at different times of the day, and under different condition (wet, dry, full sun, shadows, reflections, etc). So the general concept stuff I gave you still applies. But only you can apply that to what you're seeing on site.
Based on these new pictures (and my computer and monitor), all the materials, the samples
and those installed, all look like they belong to a pleasing palette. That said, the less color there is in the coping, (the more white it is), the less visual tension will exist (if any does), because white goes with anything...
Keep doing what you're doing. Compare samples in your own yard. Stare at them for a few days. One of them will speak to you. And when you settle on the material, if you decide to reinstall the coping, then my tips about laying it out and arranging all the pieces yourself would still be a good idea. Even if the new tiles are all a consistent color, going through each piece yourself will assure you that no clunkers get through. Like those with weird textures or cracks or chips. You're basically looking to eliminate anything that might bug you later. Things that wouldn't necessarily bother the tile crew, that they won't even notice.
To answer your question, no, I've never dealt with replacing coping myself, but others here have. So I know it can be done. It'll be quite a demo process, for sure. If you do lay out the new tiles yourself, you should number them on the back side, as they will get moved for the demo and your careful considerations of which go where will likely get lost in the shuffle. If numbered, the tile setter will have an easier time of restoring your layout work. You could even include an arrow, that points at the pool, so the installer will have no question about which direction to lay each tile.