The 1862 Pocket Navy and Police have exactly the same frame, with the rebate step. Though the fluting somewhat disguises it, the two cylinders are interchangable, both are rebated. Other than the normal fitting required of a spare parts stock, they are completely interchangable, and were you to purchase an 1862 Police and spare cylinder and barrel for an 1862 Pocket Navy, you could convert the gun back and forth with no problem, except for minor fitting of the wedge and cylinder gap.
As far as I can tell, the fluting was done for appearance and perhaps for weight reduction. It is a better fluting on the 1862 than on the 1860 and 1861 as they were fully fluted, and the bolt timing is extremely critical or it stalls the revolver if the bolt drops early. The 1862 locking notches are on a cylindrical surface with the half fluted portion forward, so the timing is more forgiving.
If you mount a 31 caliber barrel on an 1862, you are advised to also use a 31 caliber cylinder. It would be better to shorten an 1862 barrel than to go to the expense of reboring the 31 bore if what you want is a shorter barrel.
Pietta does not make a small frame revolver, and Armi San Marcos is gone. That leaves Uberti. VTIgunparts stock the Uberti parts, which will fit all the 2nd and 3rd gen Colts, sometimes better than the factory parts in the case of the 3rd gen.
I recently bought a set of barrels and cylinders from VTI to recalibrate my 1872 Open Tops from 44 (Special and Colt) to 38 Special. After a quick lathe turning to set the endshake and cylinder gap, and adjusting a wedge, they functioned fine last Sunday at a match. Now I can interchange from 38 Special to 44 Russian with ease, and saves the expense of two additional revolvers. The open top Colts are great for that, you can buy longer or shorter barrels, or cut them if you buy spares, and change barrel lengths as you please.
Filmokentucky seems to have similar experiences with the guns as I've had. They are a tinkerer's dream.