(Extremely late to reply to this but you know what, better late than never)

I might explain their history but nothing is official and I'm doing this with what I already know.

(Note : the time in BB : The First Blood isn't specified and the best we know is that it takes place in a post apocalyptic era so the time in the events I'm about to tell is really blurry)

Here's my brief interpretation of their history

Pre Doll Invasion

The first skull minions have been invented by Walz Dizzy. Nothing is known about him but since it's a "parody" of Walt Disney, I'll assume he has a similar story.

Walz originally invented them for a personal and/or humble purpose. But then one day he has decided to show his first skull minion to the world. A certain toy industry got interested in this idea and started to make a brand out of it, and called them "Kikky" to commercialize the toy (which is the skull minion's names in the game).

This made the Skull Minion project strip away from its original purpose and to be a marketable toy. The company has profited a lot from that brand with is economical success...

Years later, Dizzyland has opened its doors in Japan due to the popularity of Skull minions.

Things were looking like it could go well, but it didn't last until the doll invasion.

Post Doll Invasion

After the Doll Invasion, several people were speculating on whether Walz Dizzy is alive or not. Many rumors have been spread about him. Many say that he's still alive, others say that he died during the invasion, and others say that his soul has been posessing a doll vessel, but the his current situation is still unknown.

The dolls have built a statue of Walz Dizzy in Dizzyland in his honor. In honor of the one who started it all.

And that's the brief history of the Skull minions