The live oak will certainly outlive and outgrow the water oak, and will eventually solve the issue on its own. Rushing the process with an immediate removal of the water oak will suddenly place the subordinated live oak in full sun, and subject it to possible sunscald.
Perhaps reduction pruning of the water oak would give the live oak a chance to more quickly prevail in their race for the sun. Once the live oak begins to overshadow and suppress the water oak, you should basically be able to stand back and watch the live oak solve the issue on its own.
The live oak has some pretty significant lean, bow and sweep going on. If it puts out any epicormic growth opposite the direction of the lean, it may be a good idea to encourage growth with good attachments, to cultivate better symmetry in the canopy over time