In case you don't actually need to do a shuffle (your three constraints do not mention it, only your implementation) you can consider a simple rotation (untested, perl not available at the moment, some parentheses or corrections may be needed):

push @$_, shift @$_ for @nums;
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OTOH, if you actually need shuffling, note that your approach only works for an even number of columns, so you should at least arrange for a final swap between the element whose index is the last in @cols and, say, the first column. Another question that popped to my mind is why you do that half-slicing, instead of considering adjacent elements.