The Yam / Suz / Tohatsu branded ones have an "acess plate" along the bottom of the side that is shown in your picture that gives acess to the cable mounts. Looking at the pic, yours may be a different case design, and so you may need to split the case (carefully) to get inside. The cable sheaths will be slotted into a groove near the exit point, and the inner core will be circlipped to two pins on the operating levers.
Should you have to split the case, make sure you find the side that is obviously a "lid" (probably the side we're looking at on your photo), and do it on a horizontal surface. Depending on the age of it there may be a small plastic bush drops out, and the other to watch for is a steel bush that runs in the groove on the main lever cam (will make sense when you open it), both of which have a habit of dropping out if you take the mechanism apart, but you shouldn't need to go that far inside.......
Then it's just a case of swapping the fittings from the old to the new cables, and reverse above procedure! Also if you end up totally dismantling it, you may find the "official" entry hole for your PTT switch cable.
Engine ends of the cable are better clamped in (due to turning & vibrations) but apart from that, it's a similar story - lid off, find the bolt that holds it all in place at the end of the sheath, undo! You may need a set of "mariner" fittings to connect the cable, but having said that, the place that sells you the new cable should be able to help you out with them.