That's not quite right: your method sorts case-sensitively (uppercase first) on the first letter, and otherwise sorts case-insensitively. Whether the OP wanted the sort to be otherwise case-insensitive is not clear, but he did ask for lowercase initial letters to be first.

Here's a fix:

sort {
   $b=~/^[a-z]/ <=> $a=~/^[a-z]/
   or lc($a) cmp lc($b)
}
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