Thanks for the feedback! You can cycle with Z, but too much control over your hand would be overpowered. To an extent I wanted you to have to make do, while still having the ability to reject a card at the cost of a turn, and making it an important tactical decision between whether cycling is worth that lost turn (in which you may get hit).
Since you mention pressing enter to burn time instead of using Z, I'm going to update the help screen to use "cycle" instead of "discard" as the terminology since discard may be misconstrued to mean permanently destroy. edit: this is done as of v1.1