Alternatively, if you can get your hands on it, List::MoreUtils has a bunch of small, but useful subroutines.
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use List::MoreUtils qw(any);

...

print "Success" if any { $_ eq "correct_value" } @hash{@array};
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Notes:
1 - note the use of a hash slice; it takes some getting used to, having a @ instead of a % in front.
2 - please use something more meaningful than %hash or @array as var names in your actual code :)