You don't have to drop the transmission, but it is a job to remove and replace the belt. The Clip Director system unfortunately adds a lot to the process. You also need a torque wrench to set the correct tightness on a few fasteners (blade bolts, pulley nut, etc.to do the job correctly
You must drain oil, fuel, remove blades, remove the rear scroll and belt cover assembly, remove the Roto-Stop assembly, return springs, cable, drive pulley, drive cable, return spring, remove input pulley flange nut, etc.
Really best if you get a shop manual to have all the details. Here's a link to get one; you need to know your full model name (look on the data sticker on the back of the mower deck):
Honda Shop Manuals -eBay
Most mower manuals are $35, and you will earn that back the first time you DIY vs. pay a dealer to do any work for you. Price includes free shipping too.