Can I use a threshold to avoid 0 p-values

Question

I have many kmers counts from different prokaryotes, and I use a high markov order to obtain the expected counts to compare with the observed counts. And for look for over/under represented kmers counts I use z-scores. From z-scores I calculate my p-values and then e-values. So Iuse threshold e-value = 0.001 to select the extremes words/kmers.

However I got some 0.0 p-values/e-values for very extreme z-scores, due underflow.

Can I use a p-values that do not cause underflow to avoid the 0 values? For example, 1.0e-323 (the one that do not give 0 in my machine) when the p-value is zero? like: if p-val == 0, then 1.0e-323 else the p-val non zero? I use this function to calculate my p-values:

pval <- function(kmer_list, kmer_data){
    n <- nrow(kmer_data)
    for(i in 1:n){
        zsc <- kmer_data[which(kmer_data$kmer == kmer_list[i]), 
                 "Zscore"]
        pval <- pnorm(-abs(zsc)) * 2
        **# maybe the if statement as above?**
        kmer_data[i, "Pval"] <- pval
  }
    return(kmer_data)
}

This solution is a valid statistical approach? Or I don't care and keep the zero p-values and zero e-values anyway?

I really appreciate any input.