According to the Remington Model 1894 serial number chronology the late Charles Semmer produced from surviving shipping records, for his book
Remington Double Shotguns, your gun is of late 1905 vintage. Here is the Trap Gun page from the 1905-06 Remington Arms Co. catalog --
1905-06 Catalog pg 11, Trap Gun.jpg
While the Pigeon Gun listed in the 1902 catalogs and the Trap Guns shown in the 1903-04 through 1909 catalogs are pictured with a safety I have recorded half a dozen "no safety" Remington Hammerless Double --
1906 CEO Pigeon Gun.jpg
all the later style action with separate firing pins.