Hi,
The clutch is not in the tranmission. It is in fact on top and the input sheave to the trans is a part of the clutch.
I have no idea how mechanically inclined you are, but do understand that these mowers were over-engineered. Things to do with them can make a good mechanic cuss. I have not repalced a RER clutch, but I have said a few choice words at some of them and even more at some of the lawn tractors.
You can get a copy af the owners manual by download, but you would have to buy a service manual.
At any rate you can expect that the transaxle has to come out of the machine.
Parts are notoriously expensive!
A rule of thumb of any of the Honda riders is: "Do Not Wash Them" unless you want electrical or clutch problems, or both. The same would apply to leaving them out in the weather.
For manuals:
Honda Power Equipment - Operator's and Owner's Manuals
And choose Riding Equipment, then Riding Mower and your is the first; just click "All" under Download.
Peace,
Clarke