In an attempt to keep the spreadsheet as narrow as possible whilst still displaying all the data/text in a cell/column,
can I format the columns in a spreadsheet to be say just 2 characters wider than the widest data/text entry in that column?
Yes, most of the time you can do it - there are exceptions, but they are rare.
Unfortunately, the width of the columns is not measured in characters, but in the usual linear units - centimeters or inches. This is due to the fact that, for example, a column for two 10-point wm characters will be 864 (0.86 cm) wide, and for the same 18-point letters, it will be 1337 (1.34 cm) wide.
If you can calculate how much you really need to add to the optimal column width, then use the Format - Columns - Optimal Width command and its Add parameter
It might be worth considering that if the entire column is formatted to a specific font size before the optimum width is defined AND the cell format is defined with an alignment indent then the cell contents will always be the defined indent wider than the physical point size contents.
This works automatically for left-aligned contents but the user can also create a custom format with leading or trailing spaces and assign that format to the entire column - which will automatically be represented by a blank space preceding and/or following the visible cell content.
Also, be aware of the impact of proportionally spaced fonts.