Instead of map, you can use an inner for loop. Here, the inner loop adds four td's to an array (@table_cells). It then wraps @table_cells in a table row with Tr:

use File::Basename;
# ...
while( my @cols= splice @files, 0, 4 ) {
  my @table_cells;
                                                                      
+          
  for( 0..3 ) {
    push @table_cells => $cols[$_]
      ? td( submit(-name=>'file', -value=> basename($cols[$_])) )
      : td( ' ' );
  }
                                                                      
+          
  print Tr( {-align=>'center'}, @table_cells );
}
[download]

Or, again, use the distributive property of CGI's HTML functions:

while( my @cols= splice @files, 0, 4 ) {
  my @table_cells;
                                                                      
+          
  for( 0..3 ) {
    push @table_cells => $cols[$_]
      ? submit(-name=>'file', -value=> basename($cols[$_]))
      : ' ';
  }
                                                                      
+          
  print Tr( {-align=>'center'}, td(\@table_cells) );
}
[download]