can, even ignoring the sound level, you seem to be under the mistaken impression that the spitzer bullet will give you maximum performance due to its external ballistics. This would only be true if you are shooting from a rifle with a large volume high pressure case. Your could than optimize the round to deliver good long distance performance with your spitzer-boat tail (it still wouldn't make any difference at short distances where spitzer rounds have no advantage).
But you're trying to build something to be shot from a short barrel with a low pressure round with very limited case volume. You never get the spitzer bullet to the speeds required to take advantage of the properties due to your unfavorable internal ballistics.
The third "performance" issue is that the gun would be pretty useless as self defense weapon (the main use of derringers) due to lousy wound ballistics. Rifle bullets, even soft points and other easily expanding constructions, need a certain velocity on target to expand. At the slow speeds you can achieve with a short barrels you'd be shooting the equivalent of a fmj regardless of what bullets you used.
If you really want to continue the thought experiment, start with a well defined goal (like maximum energy out of a derringer-length barrel at 100 yards). Then use
JBM's Trajectory calculator and
Hodgdon's Reloading database to get an idea if it's feasible.
After that you can propose a load that would fulfill your requirements and ask someone to run it in Quickload. If Quickload confirms the load performs as predicted at reasonable pressure, than someone might actually be willing to whip up some cartridges and test them for your. But do your homework first, there are plenty of resources on the web.