I can tell you my own speculation based on 35 plus years of collecting antique pocket knives and studying lots of old knife catalogs...
It appears to me that the trapper pattern as we know it today did not show up until the 1920's. From what I have seen KABAR and Case were the first two companies that made the "54" style trapper pattern. These two companies had family ties and many of the patterns produced by the two companies were similar. If I had to make a guess I would say that KABAR came out with the trapper first in the 1920's and Case followed.
The predecessor to the modern trapper was the "slim jack" or "slim dogleg jack" usually about 4" closed with a long slim clip blade and a pen blade. Some collectors refer to this pattern as a "pen trapper". Many of the older cutlery companies produced this pattern as far back as the 1880's including NYK, Ulster, Schrade, Napanoch, Challenge, Miller Brothers, and Utica.
It appears that at some point some companies modified the "slim dogleg jack" pattern to include a long spay as the secondary blade, creating a slimmer version of the trapper pattern. But it was Case and/or KABAR that created the first true "54" style trapper as a beefier and mor stylized version of the slim dogleg.
Given the extreme popularity of the 54 style trapper pattern today and in the last 20 years or so, it may be a shock to today's knife nuts to find out that in the pre WWII years the trapper was a relatively minor pattern. Case and Kabar made them, but early examples are relatively rare from these companies. It was close to WWII before other companies like Schrade and Camillus offered a trapper pattern (these two companies used a smaller frame than the 54).
Remington of course made the famous "Bullet Trapper" pattern which was widely sold...so if you count that as a trapper then it was arguably the widest selling trapper pattern made prior to WWII.
Prior to WWII, the pocket knife lines of most knife companies were dominated by basic jack patterns and stockman patterns. After WWII as knife companies retrenched to face a changed market, the jacks started to fall away but the stockman still dominated.
Part II later....