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It might seem a bit boring, but it would be totally safe, require no use of any Perk points or finding any resources or building anything - similar to just playing computer games or watching TV all day in today's world, sorta. This will replicate your fear and bother with radiation and survival in general.
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One is to simply stay inside your original Vault, which may have areas where there is no radiation.
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I haven't played the game, but if you don't want to collect any resources to create radaway or a food that reduces radiation, or a perk since that wastes another perk point, or build the arch (which surely must use up something), there are several thematic things you can do.
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