The variables you mention don't allow us to predict anything, as tomacropod notes. Maybe it's more useful with Campy Record, but Shimano has had lots of different BB spindles for various groups over the years. Sheldon Brown has lots of data on what bottom bracket size goes with what crank, but he only has data on the Record 9-speed. http://www.sheldonbrown.com/bbsize.html#campagnolo
If you have the original bottom bracket and can measure it, then you need to decide (or mention to us, assuming you've already decided) whether you want the outer or inner chainring to line up with proper chainline. Then do the math (typical fixed chainline at 42.5mm, whereas most road cranks measure 43.5mm to the midpoint between the cranks
. Keep in mind that a BB spindle has a right and left side, and only half of the spindle length is accounted for by one side.
Also, be aware of the chainline measurement of your rear wheel. Ideally you'd put 3mm of spacers on each side of the axle to go from a typical 120mm-spaced fixed hub to a 126mm-spaced frame.
Finally, it may well be cheaper for you to sell your Record crank on eBay and buy a different crank to set up your fixed-gear bike.