I'm looking for dramas/movies with dumb puppy leads. Examples of those kinds of leads are: Louis in Shopping King Louis or Shim Chung in Legend of the Blue Sea

Maybe dumb isn't the right word... misunderstood? Puppy leads. A lead which reminds you of a puppy... legit can't explain it any other way.

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Lucky romance (male lead - not dumb but innocent, naive)
nodame cantabile (female lead)
heart to heart (not as light hearted as the others, but a giddy feeling cute love)
Omg, I love puppy leads (esp when they are males hehe--so refreshing after too many jerk leads)

Twenty Again 
I Hear Your Voice
Baby-faced Beauty
Bride of the Century (both leads, really)
My Girlfriend is a Gumiho (female puppy lead)
Love in the Moonlight (the female, in the first half)
A Werewolf Boy (movie)

Hope you find them puppy-like!
King of High School Savvy (male lead is pretty puppy-ish, also same actor as Shopping King Louis)
Flower Boy Next Door (male lead, Enrique is kind of the epitome of dumb puppy)
Reply 1988 (Kind of everyone, really)

Hogu in Hogu's Love is a bit of a puppy, I'd say :)
V-Focus : the male mc in the second couple is like a puppy. It's a taïwanese drama so this second couple is nearly as present as the main one.
Page Turner: the male lead isn't the sharpest tool in the shed, but his heart is in the right place :3
(kdrama with only 3 episodes)
I think you're going to like these male characters from:

Falling for Innocence
Flower Boy Next Door
Kill Me, Heal Me
She Was Pretty
From Five to Nine
It's Okay, That's Love
Jealousy Incarnate (definitely this one)
Love Me if You Dare
Mask
Marry Me, or Not?
Monstar
Oh My Ghost
W- Two Worlds

For female lead:

The Master's Sun
Twenty Again
Surplus Princess
My Girlfriend is a Gumiho (definitely)
Good Morning Call
You Who Came from the Stars
Cheese in the Trap

Give those you haven't seen a try! :)