The gun in question has the later style action, so probably would have had the flat butt plate. The K-Grades were never cataloged with anything but the half-pistol grip.
Through most of the production period, the A- through C-quality guns were only cataloged with the half-pistol or full pistol grip, but we sure don't see many with the full-pistol grip. There was the straight-gripped CEO-Grade Pigeon or Trap gun though. The D- and E-quality guns were cataloged with either a full pistol grip or a straight grip. By the 1903-04 catalog the E-quality guns were also offered with the half-pistol grip. By the first 1906 Remington Arms Co. catalog the D-quality guns were also offered with the half-pistol grip. Beginning in the 1908 catalogs the A-, B- and C-quality guns were all offered with straight, half or full pistol grip, though for the A- and B-quality guns they never got "straight" into the text, but they pictured a straight gripped AEO- and BEO-Grades.
For very late guns, from 1910, when Remington Arms Co. was finishing up orders and getting all their inventory of break-action guns out the door for the sale to Norvell Shapleigh Hardware in St Louis, I believe one can expect all manner of combinations of parts