SeaRay's usually come with Mercury engines. The control is likely a Mercury, but could be a compatible independent control OEM like Teleflex. See if you can match it up and get an set of directions. OEMs want you to be able to install new cables.
You can try some generic methods to see how it comes apart.
My '98 universal control has a set screw that holds the throttle handle on. You need to put the handle in near full reverse, and a slot is revealed on the bottom of the control handle. It takes an allen wrench. Once the handle is off, the trim panels will come off and the mounting screws are revealed.
On my '88 SR, the throttle-only button would pop out revealing a nut holding the throttle handle on.
