Is there a replacement for small p-values in big data?
There is no replacement in the strict sense of the word.  Instead you should look at other measures.

The other measures you look at depend on what you type of problem you are solving.  In general, if you have a small p-value, also consider the magnitude of the effect size.  It may be highly statistically significant but in practice meaningless.  It is also helpful to report the confidence interval of the effect size.

I would consider this paper as mentoned in DanC's answer to this question.