Addons can cycle spells through a secure button in response to other secure buttons being hit, and that same button can be used to cast the current spell.
This addon uploaded just this week does what the OP wants except it's for two spells per button and not more.
There's also
this one for more than two, but it doesn't have a way to cycle through entries without right-clicking. But after seeing this thread and the surprising interest in the overall method, it's something to consider.