You can't, not in current Excel.
Actually, you CAN, but you can only change one of the existing 56
colours in the workbook (including the 16 chart colours below the main
40 in the Format Cells dialog), not introduce more than 56 colours.
You can't do it through the Format -> Cells dialog, but you can go to
Tools-> Options -> Color, select the colour that you want to change,
and select [Modify]. This doesn't brng up the wheel, but rather a tab
dialog which allows you to set the colour in question to any RGB
value.
This will affect the current workbook only.