Will this work with the Regalia (54044) 4 speed fan?

No, Hunter has confirmed that it does not make a four speed remote control.

I couldn't find a remote for a 4 speed fan so I installed the hunter remote for a 3 speed. I keep the fan swith set at high and just use the top 3 speeds. Works great. I assume it would work for lowest 3 speeds if you set the fan on the next to highest setting with the chain.

Thanks for your question! At this time, we do not make any 4 speed remotes. We are in the process of further upgrading our remote controls. We do, however, make a 4 speed wall control. It is model number 27183. It has off, Serenity Speed, low, medium, & high speed slide controls. It also has slide control light dimming & a preset set feature that keeps your fan & light at your desired settings.