The frames and backstrap/trigger guard used on the 1861 (New Model) Navy were identical to those used on the 1851 (Old Model) Navy. As has been pointed out, Colt did make a few 1861's with provisions for a shoulder stock, but by the time they did this the option was no longer as popular has it had been. If you want to duplicate the stock on a modern reproduction, order the stock intended for that maker's 1851 Navy. First though, be sure there is a notch at the back/bottom of the backstrap.
Should you fire a stocked revolver, hold it so that the weak hand is held in back of the cylinder's front. Otherwise a chain-fire could do some real damage to your hand.