I don't see any recommendation in the Honda manual. You may have to contact a Honda service center and ask. The only thing I'd be concerned about is there could be brass or bronze bushings in that gearbox, and so you'll possibly need to pick a lube that is yellow metal safe.
I have a regular grease zerc on my Troy-Bilt. It also has a little plastic plug on there too. I just pull out the plug, pump in some grease, wipe off the old stuff that came out, and I'm done. No problems so far after 21 years.