With his previous crew, the one he'd chosen and groomed himself, he could have assured her that even if they'd never had a woman sleeping in the same room, they wouldn't have dared to try anything without risking his wrath. This crew came with the ship; while he can tell that they're fine sailors, he can't say much else about them.

"Aye, you could put a hammock in the galley. You'd be warmer there anyway, with the stove there. I'll show you."

He leads her across the deck to a hatch. As they pass one, he indicates it, and mentions in a casual tone, "My cabin is there. The hold and the rest of it are reached down this way." He opens another hatch and leads her down an open ladder to a room containing a few long tables and a cookstove. "A hammock would fit in the corner there."