I'd get something like Logitech K380 or K400 Plus and a case.
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I agree. I have the k400, it would be perfect. The integrated track pad would be value added in OP's case.
Hadn't considered the trackpad. Thanks.
Probably something small and slim, like the Logitech K380.
I'd avoid the mechanicals because you're not typing anything for long and I'm guessing space will be a premium in your backpack. The K380 is thinner than any mechanical, even the slimmer low-profile ones. Plus it'll be within your budget; anything decent will not be US$50, or even US$100.
What's your budget and how are you with small keyboards, like 40%?