TLDR: You would be shocked at the tiny defects inside bullets that cause accuracy problems and how small the CG offsets and weights that are involved really are....
ETA: It takes on the order of 3 to 4 grains gross weight difference to get a 30 fps difference in the ES of a 180 gr class long range bullet, so we are not discussing fancy lab scales here.
A long time ago, in a place far far away....
When I was still very young and starting out in the defense business, there were folks who were way deep down inside the rabbit hole who were way out in front of the accuracy game and bullet details.
If you ever sat and spoke with folks like Walt Berger, Harold Vaughn, Bill Calfee, or the folks who were from The Old School of accuracy work via The School of Hard Knocks.... They would be able to sit for hours and speak about concepts that make one bullet accurate and the other a piece of trash.
Some of them would allow those of us from the defense industry to do their dynamic analysis for them in terms of the mass properties of their bullet designs. At one point I was wondering if an Eddy Current method I was using could be used and they told me it was already being done.
There was also a fellow named Verne Juenke who was a pretty sharp character who took it to heart and invented an machine that would "inspect" bullets using a concept that we also used on metallic components like critical ball bearings, gyro masses, tiny turbines, etc.. He produced and sold some of these for accuracy folks to sort their bullets.
Now to begin with, benchrest bullets in those days tended to run from little 20 cals to 30 cals, with 22, 6mm, and 30 being popular among the folks who were very serious and hand made their own.
The weights of these bullets was never very much and to understand how tiny the CG offset and inertial axes defects we are discussing takes a long time, so I will just say small, very small.
This machine would use an electromagnetic field effect to detect the oscillations of those errors while the bullet sample was spun. Because I was also concerned with spinning tiny parts at 6 to 7 digit RPMs it got my attention.
This was a cottage industry analog inspection tool made by a hobbyist that actually worked as good as the ones produced by major companies and defense corporation laboratories. It would help a user sort bullets by limiting the spin axis and CG defects. These were very small fractions of the total mass and inertia that were being detected by an inductive transducer while the machine spun the bullet.
I'll post a picture of one of them for nostalgia sake.
I lost track of Verne, but we have lost folks like Walt, Bill, etc., and they are missed.
Carry on, but before you worry about fingerprints on your bullets, worry more about how many times they have been dropped in shipping. Your fingerprints will not matter once the primer starts up, but if the internal mass properties are not good that bullet will not go where you point it. YMMV