It’s difficult to prove a negative, but nevertheless I think it’s fair to say that no, the Hyper key doesn’t have a symbol. It wasn’t present on many keyboards; the two I’m aware of are the Space Cadet and the “simplified” Symbolics keyboard, both designed by Symbolics for use with Lisp Machines. These spelled out all their modifier keys on the keycaps (Ctrl, Shift, Meta etc.).
The only modifier keys with common symbols are Shift with the large arrow ⇧, arguably Meta which was represented as ◆ on Sun keyboards, and the Mac-specific ⌥ Option and ⌘ Command keys. Ctrl is often represented using a caret, ^, but I’m not aware of many keyboards actually using that (perhaps unsurprisingly since the caret itself typically appears on a key, used to produce a caret or a circumflex accent). The other symbols used on modifier keys in Wikipedia’s “Key top” template (created in 2015) aren’t generally used and might well be Wikipedia inventions.