Re: 1959 35 'rude
TD, the simplex box in your second photo was made both for the set screw type cables and for the swaged cables. If it was made up to and including 1978, yes it does take the same cables as the older box, as depicted in your first photo. If the unit is a 1979 or newer, however, the older cables will not work.
The primary difference between the two control boxes is in the Casing Guides for both the throttle and shift cables. In the older units, they contain the set screws that secure the end of the wire in the cable, while in the later model, there is merely a hole, through which a screw/nut is used to secure the swaged end of the cable. There is also a plastic block that fits into the shaft of the handles (Casing Guide Insert), that is a different size. Finally, the throttle and shift levers have a square hole in them where the Casing Guide Inserts fit - those holes are a different size as well, so that they can accomodate the Casing Guide Inserts.
Any of the three systems (2 set screw end boxes, 1 swaged end box) will work on the '59 35hp motor. This is true because, regardless of how the fittings on the motor end of the cables are secured to those cables, they fit on the motor the same way.
PS: For the benefit of the OP, who may not know this, both of the control boxes shown in TD's photos were made in Johnson and Evinrude versions. They are identical except for badging - the Johnson versions were called "Shipmaster" controls, while the Evinrudes were called "Simplex" controls.