[shu]

just conjecture, here.....

as bullet mass decreases, acceleration increases (f=ma);
but as bullet moves, combustion chamber volume increases, so f decreases,
and so does combustion efficiency.
answer is, the lighter the bullet mass, the faster the appropriate powder.
in your case, the fastest powder available: tightgroup good, bullseye maybe better.
very little will be needed.

if you are looking for an extra-ordinary low mass projectile at extra-ordinary high velocity, you may find the barrel twist inappropriate.
any out-of-balance moment of inertia (lack uniform mass distribution about axis of rotation) at higher rotation would result in decreasing accuracy and tumbling.

since you are interested in short range target only, a smoothbore barrel may be appropriate.
(a lighter projectile with large frontal area will be slowed more rapidly by energy transfer to the air in flight, so long range application would be problematic.)

the answer, avoiding legal problems of short barreled smoothbore weapon, would be to use a slightly undersized projectile backed up by a gas check or some kind of wadding, very lightly crimped or possibly sealed with grease.