Biff...the pic below shows some testing I did last summer, shooting into a swimming pool. The tests were done with my wife's S&W 637-2 to test relative expansion of various .38 Special +P loads. All loads were chronographed and the velocities shown were the average of 5 shots at 12' screen distance. The revolver used has a 1-7/8" barrel (virtually the same as your derringer.)
Also, one bit of caution, factory velocity data is often optimistic to say the least and is affected by the length of the test barrel used. Individual guns vary as to velocity, of course, but the data I've included here was chrono'd by me in my guns, on a hot KY day.
BTW, the Federal 129 gr JHP Hydra-Shok +P Tactical load chrono'd 840 fps from the 2" barrel. (Forgot to add it to the pic captions.) This same load chrono'd 951 fps from a 3" Chief's Special .38 Sp. The 3" barrel produced 921 fps with Remington's 125 gr .38 Spl +P JHP factory load.
I don't have the velocity of the Winchester 125 gr Silver Tip JHP +P bullet.
Before anyone get's their skivvies in an uproar, I'm well aware that the water expansion medium does not equate to human flesh and bone. I used the pool because it would allow me to have the same medium for all shots, and allow recovery of the spent bullets as well as offer a look at comparative expansion.
I've posted this photo before...hope it helps...Rodfac