First of all, did you read this thread on what makes a sound funny?
Not so much an answer as a riff: Might one answer boil down to literalism? To my brain, "dry comedic" evokes quite literal sounds that are simply very well timed or cleverly juxtaposed (or inserted to infer off-screen events). Likewise, "slapstick" for me evokes vaudeville, which was a huge influence on early animation and film, where we hear utterly non-literal sounds (like horn honks, cymbal crashes, or slide whistles) that nevertheless underscore diegetic action. There are lots of sounds that are right there on the border of realism; whooshes and impacts are great examples of sounds that can go either way, depending on their implementation. My gut reaction is the difference the emphasis and distance from representative sound (i.e., see a [foo], cut a [foo]) is what could differentiate dry comedy vs. slapstick.
(Having said all that, though, I wrestle with films like Something About Mary, which was pretty much straight slapstick - was that really slapstick in its use of sound?)
But this could all just be an exercise in semantics if this isn't what you meant in your initial question - that's just my interpretation. Roger's points are excellent, although I'd add that some sounds can carry emotion if they're cliches or tropes (like the slidewhistle), making their meaning entirely culture-specific, and that it's how and where sound is used that is where the emotion, if any, is delivered.
Ahem, wow, talking about comedy like that is totally unfunny. I've gone and harshed my own mellow...