An interesting question, of course, the following is just my opinion. I can't determine if the 870 was actually for sale in 1949 or if it was designed in 1949 and first sold after 1950. If it was not available before 1950 than the literal interpertation of the rule is no;if avaailable in 1949 then the answer would be yes. In either case it is very close to the cutoff.
There is also the question of costume and persona, for the late 40s "Bugsey Segal" era, later wapons would be appropiate, for the early 30s or 20s, much less so. But the focus is really on fun and not strict historical accuracy. I myself, used a Thompson 1927A1, M1911A1, and an Ithaca M37 trench gun ( a WWII style military shotgun) as my Win model 12 was at the gunsmith. The Ithaca, while keeping with the rules, did not really fit my persona. I should add that a shotgun is not required at this time for Zoot shooting.
For the rifle side match, I used an M1 Garand since it was the only pre 1950 rifle I had fired in the last 6 months. I plan to replace it with a U.S. M1917 rifle as I want to shoot a period bolt action rifle. For the pocket pistol, I used a 1938 vintage Walther PPK, an available but uncommon gun in the 1930s. Next time I plan to use a Colt 1903 in lieu of the Walther.
So the best answer is to bring guns, experiment, and have fun. I like Zoot shooting because it gives me the opportunity to do more than plink with some great vintage firearms, i doubt i will ever have a "set" of gus, I'll always be switching around. An expert on both guns and Zoot shooting is G-man.