This is the best I can think of for an unconventional retro character in the vein of Mr. Game & Watch and R.O.B.
Instead of the laughing dog from Duck Hunt… you control the duck! They're technically the stars of the game, and they have a trophy in Melee. The name of the character would be "Duck & Dog," or something similar, and you move around as a duck with an AI-controlled dog sneaking around behind you (think Ice Climbers).
However, the duck only attacks directly with its standard attacks — pecking, wing flapping, and stuff like that. Smash attacks see the dog grabbing the bird around the neck and swinging it in various directions, but if you separate too far from the dog, you can't use these (think Olimar).
Standard Special Move - Zapper
The dog fires an NES Zapper as the duck narrowly avoids it by flying up.
Side Special Move - Pounce
The dog crouches and leaps forward at the opponent as the duck narrowly avoids it by flying up.
Up Special Move - Flight
The bird rockets up at an angle as the dog grabs on to its feet.
Down Special Move - Pick Up Scent
If you stray away from the dog, he will sniff around, get excited, and run back behind the duck.
Final Smash - Duck Hunt
Like Snake's Final Smash, a reticle appears over the screen and you fire a Zapper. When the animation begins, the dog jumps off-screen and the duck begins flying around the stage controlled by the AI. If you accidentally hit the duck, the Final Smash ends prematurely. Otherwise, shoot the opponent(s) as much as you can in the allotted time.