Can you thaw frozen cookies in a tin without them getting soggy as a result?

The more airflow you have, the less likely is for them to get soggy. The original container is especially bad, since it will likely condense moisture on its surface while coming to room temperature. A room temperature tin will be better than the original container, especially if you don't close the lid, but still far from optimal. It would be better to thaw them on a cake cooling rack, or on a plate lined with kitchen paper, then transfer to the tin after their surface has warmed up.

If you really need to keep them in the tin (e.g. you will travel with them, or you have pets likely to jump onto a plate of cookies), you can try placing a well sized pack of activated charcoal in the tin, or maybe carefully use another dessicant such as silica gel (warning, the gel itself is not edible, and the colored versions shouldn't come near food - make sure nobody comes across the pack and thinks it's sugar for pouring over the cookies). But this is not guaranteed to work, so I would prefer the cake rack solution.