I agree with the others that using a module like Time::Piece, DateTime, or at least Sort::Key is the right way to go about this. But just for fun, TIMTWOTDI, and to fulfill your "some kind of transform" idea:
use List::Util qw/shuffle/;
my @weekdays = shuffle qw/ Monday Tuesday Wednesday
Thursday Friday Saturday Sunday /;
say join ", ", map { $$_[0] } sort { $$a[1] cmp $$b[1] }
map { [$_, lc(substr $_,0,2)=~tr/softwarehum/50411307860/r] }
@weekdays;
Update: Anagram'd
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