Grover's algorithm is pretty general, I don't think there is anything we know about that we could switch to.
Shor's is faster but more specific. It works on factoring and elliptic curves, but not on hashes. The advantage of Shor's is that if you have enough qubits, you can get the answer immediately. Grover's only offers quadratic speedup, effectively halving the number of bits in the hash function.
So for signatures we just need to switch to something like a hash-based signature algorithm, with keys having twice as many bits as we'd want against classical attackers. But we don't have hash functions that keep Grover's from working, so a quantum miner be way faster than classical miners.
Shor's is faster but more specific. It works on factoring and elliptic curves, but not on hashes. The advantage of Shor's is that if you have enough qubits, you can get the answer immediately. Grover's only offers quadratic speedup, effectively halving the number of bits in the hash function.
So for signatures we just need to switch to something like a hash-based signature algorithm, with keys having twice as many bits as we'd want against classical attackers. But we don't have hash functions that keep Grover's from working, so a quantum miner be way faster than classical miners.