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;
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.
Flavio (perl -e 'print(scalar(reverse("\nti.xittelop\@oivalf")))')
Don't fool yourself.