Remember, Caesar couldn't just leave Punk Hazard (that's what I meant by hidden. He used PH as a base exactly because it was hard to reach) and go to, say, Kaido's base and give him the poison gas weapon (especially with people like Big Mom and the Marines searching for him). He needed somebody to distribute his stuff. And considering that Kaidou was already using Doula to obtain Smiles, then why not use him to obtain Caesar's weapons while at it? Don't ignore what Robin said. Kaido's connection with Caesar relies a lot on Doula Mongo, as the latter is the one that makes the cash and products flow. That much is stated.
I'm not ignoring what she said, but Caesar is not oblivious to who his weapons go to. According to Caesar himself, he knew who put in for his Shinokuni weapon & where it was going. Smiles was created in Dressrosa which is the only reason Caesar didn't know which Yonko got it. He only produced S.A.D.