Is there as HashMap overload with three type parameters? Yes, you can use a cryptographic hash function like SipHash does but it wouldn't perform has well as HashMap.
But there is a heavy multiplier on that O(1) with the default hasher in Rust. My benchmarking has shown that FNVHasher gave me a 24% decrease in execution time over the default hasher. My use case had a high likelihood of a poll on the hash indicating that there was no match, and I got a near doubling of speed just by setting the initial capacity sufficiently large.