How do you make a sound, sound "soft around the edges?"
I know that you can compress a reversed sound and then reverse it again. Fluffy crossed with cartoon is the sound quality.
Reverb? Compression? EQ? Layering?
Try baking in reverb on a duplicate layer and mixing the dry and wet that way. Sometimes it helps to be able to process the dry and wet layers independently.
Drop some of the presence out of the sound, the frequencies humans hear at a higher volume than others because of the way we perceive sound. I believe this is based on the Flecher-Munson Curve. Look here: http://www.vettaville.nl/vvFletcher%20Munson%20eng.htm and see where it says around 500-5000hz we perceive these to be louder than lower or higher frequencies. Drop some of these out and maybe it will feel less detailed, adding to your fuzziness quality (in addition to the other techniques as well).
I know older recordings sound a lot less crisp than newer, well recorded audio. Try looking online or in your library for some old recordings and layer those in. Sometimes that thick muffled quality can be exactly what layer you are looking to add.
I know the Hana Barbara stuff is very cartoony, this library might have the more cartoony layers for your design as well.
Daisy chain compress the whole lot for 50/150ms and 150/50ms, group everything to a sub master bus and add some miniscule reverb and pull the dry signal down a bit. You might also want to try a minimal amount of chorus to that channel as well, It adds more silk to the mix but you have to be really REALLY careful with the plugin mix level...
What is your source material and what exactly is the sound for?
I have a few ideas but if I knew what sound you were trying to make more fluffy and soft I think I could give a better suggestion.