Just  shuffle the array, then take elements in order until the array is exhausted:

>perl -wMstrict -le
"use List::Util qw(shuffle);
 my @array = 1 .. 10;
 @array = shuffle @array;
 my $i = 0;
 while ($i < @array){
   print $array[$i];
   ++$i;
   }
"
10
2
3
1
8
9
7
4
5
6
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