Trip has already done this in canon - they didn't use the transporters much at first, so crashed shuttle was a staple plot. He'd take the communications panel and some tools (if that's cheating, then the tools were totally already in his pocket). He'd fix it, call Enterprise and get rescued. While befriending the locals. Even if they're not friendly.

Cat would save his clothes. If he only had what he was wearing then he'd get the gun. Or the stick with string stuck to it, if he got distracted. He'd confuse the locals by demanding to be fed and then falling asleep.