Loki would have been lying if he would have said that the fact that she took his hands and looked for signs of injury then showed obvious relief at finding none didn't amuse him. Because it did. The mere fact that she was concerned for his well-being was amusing. Didn't she know who he was? Or what he was, for that matter? Loki had always thought that while he was sort of lumped in with the Aesir, he was frequently reminded that he was adopted Aesir and that it was common knowledge that both of his parents were from Muspell.
Which was why when she remarked about how he wasn't hurt at all, he couldn't help but reply with, “Of course not. Why would I be?” He was a little disappointed when she took her hands away from his and whatever that was about needed to be nipped in the bud immediately. Loki had to remind himself that he didn't like this woman. Even if she had only been teasing him all those times, it was still a bit rude to tease at the level she did when she apparently didn't even know who he really was.
Even so, her hands had been soft and there was something relatively nice about the physical contact even if he didn't see her in any way other than someone who was stuck in a cave with him for the next day or so.
He nodded when she asked that he turn around. No matter their opinions on each other, no matter his reputation, much like when they first met and she had been only in her shift he would give her the privacy to dress or undress herself as she needed to. While the cold didn't bother him, she wasn't made of the same sort of stuff he was and was probably freezing between the cold and the damp. He too was struggling with the damp on his own clothes but was unsure what to really do about it. He wasn't shy but he wasn't about to strip down to nothing and just let his business all hang out for her to mock.
No matter how confident he was in his appearance.
It then occurred to him that he had a thin blanket rolled up tightly in his pack. It didn't really keep the damp out, so when camped out in the elements he tended to leave it rolled up and as a pillow rather than a blanket and instead would wrap his heavier cloak around him to keep the damp out. Turning around as she asked, Loki stood and went to his pack discarded over by the rabbit carcass. Crouching down he pulled a few things out of it -some parchment rolled into scrolls, various bits of foodstuffs and other miscellaneous things before tugging out the rolled up blanket. He could wrap it around his waist and solve the nudity problem.
Except there was this nagging bit of him that knew she was going to struggle with the same problem and Sigyn wasn't capable of warming herself in the same manner he was. Sighing inwardly, he did what he knew was the right thing to do.
Without turning around to intrude on her privacy, he tossed the blanket a little behind him, taking care to avoid the direction of the fire and said, “Here, that is dry.”