Honestly I'd ditch the Dock icon and keep the menubar item. For a utility with no other UI to use, that's the way to go, and similar apps do the same.

W.r.t. the history — I'm just saying I don't want my input to be logged at all. It has no utility. It can be discarded as soon as it's pasted. I don't want to maintain a log by pressing Clear every now and then.