Is there any way to computer Fisher's on SPSS for larger than 2x2 contingency tables? This is because 100% of my cells have an expected count of less than 5 and so I think a Fisher's test would be the most appropriate (unless I am wrong here). Any advice would be appreciated.

Hi. The Exact Tests module is designed with such cases in mind. See /METHOD=EXACT in CROSSTABS, for example.