{
   # Temporarily undefine STDOUT.
   local *STDOUT;
   func();
}
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as in

sub func { print("in func\n"); }

print("pre func\n");
{
   # Temporarily undefine STDOUT.
   local *STDOUT;
   func();
}
print("post func\n");
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If func checks the return value of print in the above, it will notice that print failed. If you really wanted to print to /dev/nul (or to another file) and avoid that (rare) problem, you'd use

{
   # Temporarily redirect STDOUT.
   open(local *STDOUT, '>', '/dev/nul');
   func();
}
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You can do the same with STDERR. You might also want to look at $SIG{__WARN__}.