I want to sort that hash, and print only the values for the first keys

Do you mean that for each key you want to sort the array associated with that key and then return the first (i.e. smallest value) in that array? If so, here's how to do that:

my %smallest;
for my $k (keys %hash) {
  my $v = (sort { $a <=> $b } @{$hash{$k}})[0]; # assuming numeric val
+ues
  $smallest{$k} = $v;
}
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