Don't think it'd be possible to copy stuff to clipboard directly from a mod - afaik lua api doesn't allow that.
I'd also be surprised if direct clipboard functionality from a mod was ever added, as it's OS clipboard, and people use that for all sorts of sensitive stuff, like passwords and banking details, so probably best to not enable that (ab-)use-case for mods here.
That said, it should probably be possible and easy to make variables' textbox editable on freeze, and then you can just ctrl-a/ctrl-c stuff out of there.