contigency table

I have a 2x2 contingency table, but the total sample size is too large to be able to directly apply Fisher's exact test (as it involves factorials, so I'll obtain NaN or infinity). I know I could use chi.square instead, but I wanted to provide Fisher's exact test results. Could it be...

I am looking at male-biased sexual size dimorphism in a bird species (males average larger than females). I am interested in the proportion of males larger than females in breeding pairs. I have one proportion result "A" from observed breeding pairs. I then did random bootstrap resampling...