The one way air valve means it does not need volume, just some pressure.
If the plastic mattress-thing is anything like I picture it in my mind, it does not need much pressure at all.

Leading me to believe a DC muffin fan would work just fine.

And I believe this is a case where solar would be worth the initial cost.
Mental math this morning (pre-coffee) looked like about $70 / year for the grid fan.
Solar with junk ("boat batteries") payback was about 8 years and soon to need the 3rd set of batteries.
With a pair of Sam's Club golf cart batteries was 9 years But that had new batteries figured before then that would last a lot longer than the 9 year mark, meaning golf cart batteries worked out to cheaper.

That sounds BAD?
It only included the cost of RE related items.
It did not include the cost of running the grid to the green house.

If the cost of running the grid to the green house (I used $200 total cost) is deducted from the RE related costs, then even was at 4 years 9 months.  
After than time you are coming out ahead.

If you have to pay someone to do the AC grid wiring, or the run is long, or it requires an excavator or renting a ditch-witch, then solar may work out cheaper the first time the fan is turned on.

The one way air valve has me wondering if the initial cost could be reduced even more.