The rim diameter is essentially identical to the 9mm Parabellum, so you could use a 9mm slide. The problem is the overall length of the cartridge. 1911s are built around the .45 ACP cartridge, which has a C.O.A.L. of 1.275 inches. The 7.62x25 has a C.O.A.L. of 1.386 inches, so it's too long to fit into a 1911 magazine or magazine well.
A [very] remote possibility might be Armscor (Rock Island). They offer a 1911 chambered in .22 Magnum, which is also longer than .45 ACP. They make a special frame just for their .22 Magnum pistol. I don't know how close to the limit they make it, though. The nominal C.O.A.L. for .22 Magnum is 1.350 inches. That's still shorter than 1.386 inches. I don't know if the RIA .22 Magnum has enough space in the magazines to accommodate that extra .036 inches of length. I also don't know how difficult it would be to modify the .22 Magnum magazines to handle 7.62x25, and I also don't know if the larger grip on the RIA .22 magnum would fit your hand.