A chain whip is not necessary to remove a fixed gear cog. Once the lockring is removed you can reinstall the wheel and mash the pedals backwards to break the cog loose. In fact if the fixed gear cog has been in place for awhile and ridden up hills or sprinted on a bunch it may be very difficult to remove with a chain whip unless a long cheater bar is used to add more leverage...in this case using the bike may be easier and quicker.

-j