12 Volt Fan
I just purchased one of the Ocean Breeze fans from Camping World for $60. While that is expensive in my book for a fan, when it was 111 out and I was having that warm air blast me it was worth every penny. I also have the Hella for localized air movement in the berths, since they are so power efficient and can run all night. While the Hellas are great in the berths, I found them inadequate in the salon. While you could run your 110 volt fan on an inverter, what is the reasoning for not wanting to switch to 12 volt? If you're only going to have one fan, why not make it 12 volt so you could use it while docked or out?
As for power consumption, the Ocean Breeze is a pig, consuming 3 amps on high. When my friend ran his on high all night it drained his 2 battery house bank by the next morning. The upside is it took longer for this powerful 12 volt fan to drain the batteries than it took when he a had a house fan wired through an inverter.
One more item, I think the Ocean Breeze will move substantially more air than your Honeywell. My guess is if it's a short night, and you start with fully charged batteries, you should make it through the night with the Honeywell or the Ocean Breeze, but you might be well advised to have an isolated starter battery.