Sneider & Lefever both had hammerless patents issued in 1880, Sneider's was a little earlier. Am currently away from home so don't have my list with me.
I have an interesting photo-copy of an article written by "Curtis" (I forget for sure which one) & stated to have appeared in the Rifleman back in the 40's I believe it was. From his research at that time his conclusion was the Lefever was first made in 1878, prior to its patent, & did precede the Sneider. He stated the Sneider had been credited with being earlier than the Lefever based on its addition in an earlier dated catalog, but examination of the catalog revealed the hammerless gun listing had actually been pasted in over a hammer model. This was not done as fraud, but was done by Sneider at issuance as an update, thus the catalog did not actually reflect the proper date for the hammerless gun.
Sneider did of course build the first Self-Cocking hammerless double in the US. As to which one actually sold the very first hammerless may always remain up for question.