I would not use the dimmer switch for this; even at 100% and with instant on, you’ll run into two issues: notably, the dimmer still isn’t rated to power an inductive load, but second, even if it were, the fan (and possibly lights if they are not dimmable) would likely not take kindly to being run from a dimmer, where a dimmer at 100% in my experience does not match the output you’d get from a “real” switch. You could probably get around this by hardwiring line to load at the switch/dimmer (so power to the load isn’t going through the dimmer at all, but keep in mind this also prevents the air gap from working, and I can’t speak to code requirements in your area). The switch would avoid this issue; not sure if you have a reason to prefer the dimmer, since without local control they’d function the same aside from the physical LED bar appearance.
As for the switch, I’ve only see then incandescent/CFL/LED and inductive loads listed separately, so I’m not sure they have specs as to how they could be combined. That being said, if neither your lights nor fan alone are close to the limits, you’ll probably be fine (the HomeSeer HS-FC200+ fan switch is also rated for 300 W fans, so I’d assume this would cover most residential uses). I am not an electrician or an engineer, so don’t hold me to that.
With local control disabled, you could certainly use the Red Series Switch (and maybe dimmer if you hardwire as above) as a scene-only alternative. You should be able to create an automation that listens for the scene events from the switch and uses them to send the desired command to the Hampton Bay controller (e.g., single tap up? turn on lights. double tap up? turn on fan.). I’m not using Home Assistant for this purpose but used to have something similar set up on Hubitat (not sure if you need to do anything special on HASS to “see” scenes from the switch, if that was just the dimmer, or if the changes made their way to the OZW library HASS uses yet).
That being said, if you can wait a bit, the Hurrican fan/light switch combo would do exactly what you want. The ceiling module would replace the Hampton Bay, and it would communicate to your wall-switch that doesn’t even directly control your load (both are separately powered and communicate via RF, so no separate fan/light wiring is needed, like the HBFC; the Z-Wave smarts live in the switch compoonent, not the ceiling module where the HBFC Zigbee radio lives, though unlike the HBFC, you’d need a neutral in both locations—something you’d already need for the Red Switch, anyway or the Dimmer if hardwired, the only way I’d even consider trying this).
That being said, an LZW30-SN or LZW31-SN seems like an expensive stopgap to me, though I’m sure they’d love it if you bought one, and maybe you’d have a use for it somewhere else afterwards. If you can make any button device work in the meantime, that could effectively replace a wall switch temporarily if you want Hurricane in the end. (On Hubitat, I’m using Lutron Picos with a Smart Bridge Pro, but that’s a high entry price if you don’t already have a Caséta or RA2 system. I’m not sure if HASS has better Zigbee support than the last time I tried, but if so, the Hue Dimmer or Eria Remote might also work. Inovelli announced paddle remote that would be perfect here, but it’s likely a ways off still.)