It should be pointed out that what I am going to say here will be me speaking for myself, and not necessarily a reflection of the proper covenanter position. My reasons for still participating to any extent in electoral politics are largely based on a somewhat unique understanding of the history of the church, both the early church and during the Reformation, and some of these positions put me closer to being either a Ultrajectine or a conservative Anglican, which is a testament to my family's church roots.
The principle justification for voting in this climate, particularly if you've already been registered, would be tantamount to something along the lines of Paul invoking his Roman citizenship when under duress. Granted, this is not the same thing as voting, and it would be a stretch even under the concept of Christian prudence. Likewise, the Scottish Covenanters did form an alliance with the House of Stuart when it became clear that the Independents under Cromwell were going to plunge the 3 Kingdoms into tyranny, though this proved to be a mistake given that it ended in betrayal. Non-involvement has often been the preferred route for dealing with severely backslidden magistrates, but there is historical precedence for involvement throughout history.
The most important thing to understand is that a Rand Paul presidency would be the least of all possible evils at this juncture, and probably would end with the least degree of ongoing persecution of the church, but it would be an exercise in slowing down the decline and should not be viewed as a victory for the Reformed cause. I can't say with any certainty how Reformed Rand Paul actually is, but he and his father are probably the closest thing to even nominal Christians that I've seen involved in presidential politics in my lifetime.
If you really feel drawn to the covenanter position and are having moral difficulties with the state of this country's politics, my advice would lean towards telling you to dispense with voting, but even if you decide to do so, you are not prohibited from offering advice so that others would vote for Rand since it would result in a better outcome for everyone. It's a judgment call, and I don't quite feel qualified to tell you one way or the other.