Let's break this down shall we?
1) Dan Quayle - he would be Trump's intellectual equal so the Donald won't go with another 'stable genius' on the ticket.
To digress briefly and just in case you don't know this one, let's take a trip down memory lane.
Dany Quayle, Newt Gingrich and Bill Clinton were driving across Kansas in a car when a tornado whisked them away to the Land of Oz. When they came to, they were brought to see the Wizard.
Dan Quayle said, "I need a brain, I need a brain."
Newt Gingrich said, "I need a heart. I need a heart."
Bill Clinton said, "Uhhhh, where's Dorothy?"
2) Oddjob and Gort would give the Democrats an excellent opening to enjoy developing their own birther conspiracies. But we all know that as for as the Republicans are concerned, turnabout is not fair play.
3) Sarah Palin is now 60 so are you implying that the 'boys' have now grown up and are mature enough that they prefer to grab 'em by the cat?
4) Julie Newmar is far and away the best possible candidate on this list. She is American, so now birther issues. She is not homicidal like Oddjob or Gort so won't require a messy Presidential problem at some point in the future. And she is 91 years old so her 'cat' is unlikely to cause any problems to these two stalwarts of protofeminism who are doing so much to empower women back into their rightful place in society. Also, at 91 she would be unlikely to inflame their passions in such a way as to distract them from their historic mission.
Please take the time to watch that classic film 'To Wong Foo, Thanks for Everything! Julie Newmar.