What sort of HA solution are you aiming at?
If you are intending to get a failover cluster, that is not possible without shared disks, since the whole idea is that you have two nodes that share the disk where the database resides, and both nodes can work with that disk.
If you instead set up an availability group (AG), it is a different matter, as you have local replicas of the database on each server, and the primary replicates the data to the secondary. However, a proper AG solution requires a cluster, and I suspect that the cluster still requires something shared. If nothing else, you need a file-share witness so that you can achieve quorom in the cluster.
It is possibly to have an AG without a cluster; it is a special type of AG known as clusterless. However, this does not really count as an HA solution, since all failover need to be manual.