Is it possible to construct dataset for only another party to consult?
Answering my own question. I believe it is possible. We can use the scheme by Boneh et al. described here. 

It uses pairing-based cryptography to be able to create a searchable, asymmetric, tagging scheme. In this scheme, queries are made through a trapdoor of the real key that we want to search, making it impossible for the set holder to retrieve information about the underlying queries.