Being a Harley guy, I probably won't be much help other than to say a full amp is way too much for the radio system. It's normal for most radios to pull a few milliamps, but 1 amp is too much. I can't say for sure that it's safe for you to ride without that fuse. Maybe someone else who's more familiar with Honda's electrical system can. What you can do is hook up a "battery tender" to keep your battery up, or if it's not hard to get at, plug the fuse in when you ride & take it out when you get back home. Since your charging system is working ok, it'll keep the battery charged while running. Even though a 1 amp discharge is not desirable, if your trike sets a couple of hours after being ran for a while, it should restart. I would NOT leave the fuse in overnight.
NM