Looking at the first picture, I don't see the manual lifting option at the hydraulic pump, so, I'd say you HAVE to use battery power to lift the top. That's not a deal breaker though. If you can get to the battery terminals (or add some short cables to them) you could use jumper cables from your tow vehicle to get the top up if the trailer battery is down.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew