Such gizmos do exist and there is one here in the "toy-box".
The catch would be in the realms of heat and pressure, with some concerns about concentricity.
A "paper" sabot seems a bit of a step too far.
If you are thinking of, say, .308" bullets in a .312 bore, that's a radial difference of TWO thousandts of an inch, cigarette-paper territory. making .308" bullers "work' in an 8mm / .323" barrel would need a bit more paper, but hand-wrapping these tiny bits of paper around a tiny bullet is still a challenge.
I know there was a work of fiction in which the core of the plot was taking a recovered, FIRED bullet from one rifle and "paper-patching" it to be fired in another rifle of slightly larger bore, but.........
ANY hollow or soft-pointed bullet fired, even at reduced velocity into any medium designed to slow and capture it, WILL suffer some distortion. That is what such bullets are designed to do. Try "recycling fired bullets and let us know what sort of groups result. One TENTH of a thousandth of an inch of eccentricity at the meplat will contribute to dispersion, hence the bullet fetishes of the bench-resters. Furthermore, on impact, even a "soft" one, the core tends to shift.
Now, if you are starting with good-quality NEW bullets, keeping it concentric with the rifling whilst wrapped in paper is the next challenge.
Some years ago I scored a bunch of Remington "Accelerator" projectiles and a bag of "spare" sabots. So, .224" bullets in a .30 Cal bore. Great concept, BUT. LOTS of fiddling with powders and several trips to the range. TOTALLY different point of impact; oddly enough, usually LOW. Recoil? About a third of the usual bullet weight and with the slick plastic sabot almost friction-less in the barrel for a VERY short time, almost no backthrust / recoil.
Also, in the good-old-days: TOTALLY different bore pressures / dwell time; pretty much useless in gas-operated 7.62 NATO rifles. I tried some in 7.62 x 39 cases fired from an SKS. Same wildly shifted POI and SOMETIMES operated the action. Because of the ludicrously light bullet "accelerating' very early after ignition, much faster propellants than normal are needed.
There are still several hundred of those sabot things in a box, somewhere here; an interesting bit of technical history.
The Big Kids" get to use serious ones, in tank guns. Think: two-feet long bar of solid Tungsten Carbide, (that is a LOT of grains of bullet weight), launched at a muzzle velocity of 4000 feet per second. That Rod of the Gods will punch trough almost any material and at the most spectacularly fine angles of incidence. There is a photo out there of a T-55? that has been "demised" by such a projectile striking the barrel of the main gun at an extremely fine angle. It ploughed through the barrel wall and continued rearwards to the breech and punched that out. The crew members were not available for comment.
Black-powder shooters have had "Big-Bore" saboted bullets for a while; .58' Cal. rifled muskets launching conventional jacketed .30" Cal bullets. Probably nort as cute as it sounds; BP rifles tend to have quite solw rifling twists and unless you stick to "short" jacketed bullets, stabilization may be an issue.
Paper wrapping on a different scale ~ A story from my book on Elmer Keith "Hell I Was There" or my 1969 Guns & Ammo mag where he and a friend were very young and being held by a no gooder and paper wrapped the hull of cartridge may have been a 38 in a 45 bore cannot recall they managed to squash the item into the cylinder and waited till the no gooder was just about eye to eye when Elmer whipped out the piece and in his words.
"The cartridge went off and that bullet wobbled down the bore but did the job"