You ran into a bug.
When I use 'Reply without quotes'(it's in the specials menu) while viewing a html message in html mode then my reply contains the quoted message. Apparently there's someting amiss with the html editor.

I enabled: Options -> Preferences -> Viewer/Editor -> Reply to HTML in plain text
Afterwards my plain text replies to HTML messages were empty when replying without quotes. After disabling it again 'reply without quotes' is giving me quotes.

This doesn't solve your problem, you could try this:
Create a quick template:
Tools -> Quick Templates
When you create that quick template, make it a reply template without quotes. And assign a reply shortcut to it.
Ctrl-K would be a good option as that is assigned to an action per default.
Now instead of replying with F4 you can reply with Ctrl-K when you want a reply without quotes.