The problem is not exactly with "older" devices, but with the fact the visibility property is not supported by the ePub 2.01 specification, so any device could not support it and still be ePub-compliant. On the other hand, mobi does not support CSS at all, new or old, and it has no equivalent for visibility as far as I know.
You could try to force the invisibility by using:
But opacity is a CSS3 property that's not in ePub 2.01 either, or in ePub 3, I believe. Using a white color for the text will only work if the background is white, something you can't guarantee unless you force it (and that's not nice). Unfortunately "transparent" can only be used with background color, not with text.