http://www.perlmonks.org?node_id=257200


in reply to alphabetize a hash ignoring upper/lower cases

vladb answer works fine, and I would like to add that if the code you posted is actually what you are doing instead of a simplified example, then you really don't need the keys of the hash and it can all be written as:
my @mips = sort { lc($a) cmp lc($b) } values %mips;