Is it possible to securely combine multiple hashes without hashing them?
What you're looking for is called a Merkle tree. BLAKE2b, a modern hash and an evolution of one of the SHA-3 finalists (BLAKE), supports tree hashing natively.

Edit: This may or may not actually be what you're looking for. Initially hashing the tree will take more work ($\mathcal{O}(n\log(n))$ operations) than just hashing the set of hashes, but subsequent partial updates will take less work ($\mathcal{O}(\log(n))$ operations). If you're ever updating the list, a Merkle tree is probably more efficient.