Yes. I have a cordless and corded. The first side I did with nails because I had forgotten about the corded drill and didn't want to take bits in and out a lot. I had to take that side apart twice, though, due to gaffes, and taking the nails out each time without trashing the skeleton was hard. Then I got out the other drill and used both, one for pre-drill, one for driving screws.
Interesting... another one! Going into business?

I like the wood, it allows *me* to do it [I'm one of those control freaks], and at a low cost, not very messy, etc. The trailer weighs 700lbs with all of my gear inside, so I don't think 3/8' plywood and a 2x2 frame is a bad choice. It's a lot more sturdy than I hoped, too.
Is this version going to be a camper, too, like Evas?
This trailer design & construction stuff is a lot of fun, but I'm still getting my life back on track after taking the time to do it. Let us know how yours is coming along.