Since you have the eval block there, it would seem more natural to do:

eval { no strict "refs"; &$sub_name(@args) }
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No need to turn it back on afterward; the no strict is scoped only to that block.

You can get away without no strict, doing something like:

eval { @_ =  @args; goto &$sub_name }
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but IMO that just obscures what you are doing.