If you are offended by both candidates and there is no third-party option, then not voting on this line of the ballot is the logical action. If I were in Mississippi, that's what I'd do.
I know people are mad at Cochran and the GOPe but don't vote in a Democrat. It is hard to oust an incumbent - even a clown like Al Fracken is a challenge. Who knows what will happen in the 2020 election - there could be a popular Democrat Presidential incumbent seeking re-election at the head the ticket who boosts all the Democrat candidates down the ballot or an unpopular Republican Presidential incumbent seeking re-election who weighs down all Republican candidates down the ballot. It would be a shame to see Childers become the next John Stennis and serve as the Mississippi senator forever. That's a risk you run if you vote in a Democrat with the idea of removing them after one term. A no-incumbent 2020 Senate race in Mississippi would naturally favor the Republicans.
I posted the following 6/27 and other similar post. I have used your argument for voting for rinos to others for 50 years including 2012, I have concluded it only works against us. We have to have concessions from them as they give to democrats. We cannot forgive them or overlook the tactics they used in this race.
“Speaking as 50+ year loyal Republican who has never missed an election, primary, runoff, voted for a democrat and who has worked for and contributed to Republican candidates including those primary winners or nominees he didn’t support in primaries. What is our majority in the House doing for us, they vote to spend more money, increase the national debt, fund obamacare. They have investigative committees but what has been accomplished on the IRS, Benghazi, fast and furious, VA, enforcing our current immigration laws, protecting our borders, etc.? Sure there are a few of them, I hope, who would actually do something but they are stymied by leadership and rinos. So sending a rino who was nominated by democrats who are demanding all kinds of larder being cast their way , including rescinding the states Voter ID law, is going to help?”