<span>mine are right from the dictionary:

whacko - 20 thesaurus results       absurd, asinine, bedlamite, bonkers, cracked*, crackers, daffy*, demented, deranged, dopey*, flaky*, foolish, fried*, giddy, half-baked*, idiotic, inane, insane, in the ozone, lunatic, mad, mental*, nuts, nutty*, off the wall, out of one's gourd, ridiculous, screwy*, silly, simple, touched, unbalanced, unhinged*, unsound, wacky, whacko, witless

hmmmm, I like a few of these.  I see nutty is in there so that qualifies.  So "whacko" and "nutty" are legit. 

As for perjorative, anytime you use words with the intent of belittling or disparaging, you are using those terms in the perjorative.  Calling someone unthinking or irrational is not a compliment.  It might be more sophisticated, but using "unthinking" or "whacko" are in the same camp.  The camp of the stupid. 

The words whacko and nutty can be used perjoratively or not.  The same is true for unthinking and irrational.  All have perjorative connotations.  It's a matter of opinion which may be "worse" and certainly it's a matter of style.   I think you're splitting hairs.  It's like arguing that there is a polite way to tell someone they are stupid morons as opposed to just saying it outright.  I dunno, an insult is an insult.  But I like sounding like a hack sometimes.  So whacko and nutcases and the like will do it for me.