When adding cross-references in Word there are 5 options for the result:

Each of these contains some information about the reference. If just the figure number is desired, well, none of these will do the job. This, however can be accomplished by adding additional formatting switches.

The result of issuing Insert > Cross-reference is a REF field code. To edit the field code, press Alt + F9. This will toggle the display of the document to show the contents of all field codes and allow editing. (To return to normal view, press Alt + F9 again.)

A cross-reference for a figure caption might look like:

{ REF _Ref55500687 \h }

To have it just show the number and not the "Figure " portion, add the following to the contents inside the curly braces:

\# "0"

Yielding:

{ REF _Ref55500687 \h \# "0" }

In some instances Word might tell you that picture switch must be the first formatting switch. In this case just move the \# "0" to the left before other switches.

Example: