Why not just write a function to output what you want. For example, at the start of your document, have:
<<echo=FALSE, tidy=FALSE>>=
trans = function(mycor) {
out1 = paste0("$r(", mycor$parameter, ") = ", signif(mycor$estimate, 2), "$,")
p = mycor$p.value
cutpoints = c(0, 0.001, 0.01, 0.05, 0.1, 1)
round_p = cut(p, cutpoints, labels=cutpoints[-1])
p_value = paste0("$p < ", round_p, "$" )
paste(out1, p_value)
}
@
Which allows \Sexpr{trans(mycor)}
to work as you want.