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I really wouldn't worry about it given the limited amount of contact you're likely to have in a relatively small project in those protected circumstances.
The one you linked to appears to be an MDF main board with pine stand and I suspect the only reason they used MDF for the main section was they couldn't find a sheet of pine the right size without it costing a fortune. You could get decent ply instead if MDF is a worry - some really fancy finishes possible with it, using it for the stand and main section. Typically for the super-fancy finishes you'd either be using lasers or at least a router with a lot of care but I'm sure you could get something decent done with some simple tools.
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Hmmm - I was intending to do all the work outside and with a mask. Am I actually better off using a different material?