Probably safe, but no one will write you a check if it turns out not to be. The cylinder of a .357 Mag-chambered K frame is longer than the cylinder of a .38 Special-chambered K frame, so you or the gunsmith would have to remove that same amount that is the difference. On a M-65/13/19/66, there is very little of the rear of the barrel sticking out into the cylinder window (the space in the frame where the cylinder swings into). You will also need a shorter ejector rod.
I wouldn't do it. You would be spending quite a bit of cash just to make your Model 65 worth less and harder to sell.