Well, since I lost my dealer connection, this is where I get most of the parts I use;
http://www.boats.net/parts/search/Honda/Outboard Engine/parts.html
If you look, the index pretty much stops at 1997 and just lists "PRE 1997"
Yours looks to be "PRE 1997" and I have had good luck getting parts that work for older outboards just by using the horsepower rating. If you run across something you need that has been listed as "obsolete", then just go up the year model list until you find the earliest year that the part appears as "in stock"...usually works...not always...but usually.
As far as troubleshooting your problem, You didn't say whether or not it seemed to be running in the proper heat "range". Was the pee stream from the water pump good and strong? I'm not sure what year Honda went to a EPM (engine protection module) but if that were activated due to an overheat condition it would cause a loss of power like you describe. If you have a CDI ignition, then you MIGHT have an EPM. If you have breaker point ignition, then you will not.
Other than that, things that come to mind are;
Make sure it actually getting full throttle. Sometimes the linkage or the cable is stretched or broken and the carburetor isn't being opened all the way.
Make sure that you don't have any fuel delivery problems. A tank vent that has vibrated partially closed will starve the engine for fuel. A cracked or old fuel tank hose can break down internally and an internal "flap" can develop causing a sort of valve like action to block the flow of gas just when you need it most. An old hose or loose hose clamp can allow air to enter the fuel system and starve the pump.
The thermostat is stuck open or missing and the engine is operating "cold" causing the plugs to foul. OR...
Defective spark condition caused by the above or a bad plug or plug wire.
If either of the above, you need to determine if it is running on just one cylinder. These little outboards run surprisingly smooth on just one hole. While running the engine, use a pair of insulated pliers to pull the upper plug wire off and listen for a change in rpm. If no change, the cylinder was NOT firing. If the engine stumbles a bit and/or dies, then that cylinder was working before you killed it. Remember though that they run fairly smooth on just one cylinder so you need to pay attention.
If pulling the upper cylinder wire makes no difference, then put it back and pull #2, repeating the test.
This is MUCH easier accomplished if, before you test, you first pull each plug wire off while the engine is stopped and apply a bit of DI-ELECTRIC (tune-up) grease to the inside of the spark plug wire boot. This little trick makes it easy to pull the wire off and put it back on.
If you find that one cylinder is not contributing, then it becomes a matter of finding out why. Usually a plug or a wire has gone bad. If it is a plug, that would be an easy fix. If it is a wire, then, usually, you need to replace the coil. Not so easy on an older outboard. Most of the old coils have been "discontinued" and you will need to find a substitute. Using the "next model year up" as described above can work, but not always.
If it is neither of the above, then it will either be an EPM issue as previously stated or a mechanical problem with the offending cylinder. This will require further testing as in visual inspection/adjustment of the valves and springs and/or a compression test.
If you find that the engine seems to be running ok and is not "de-powering" electronically, then you may need to carefully inspect your propeller hub. They can deteriorate and "slip" in the water making you think the engine is not running right. With the prop installed on the outboard, with the outboard in gear, you should not be able to get any movement from the prop when turned by hand unless the engine turns as well. If you do, then the hub has partially spun. CAUTION! Only attempt this check with the kill switch activated to prevent accidental firing of the engine and personal injury.
Good luck and I hope this helps.