Some ideas:

• keep all lines in memory (110,000 x 11 doesn't seem too big)
• avoid splice() and other list operations
• creative use of pack()/unpack()?
• try this: shuffle columns (1..10, but not 0) once (List::Util) for each row; then perform operations for one column after another (fixed index: 1..10)
• maybe combine shuffle and looping for each row with a suitable buffer, so you need to visit all 110,000 rows only once?

HTH