Maybe as you say it's overkill as oil will take precedence in use.
Silicon grease I think would be the right application though, it's slippery on surface but doesn't appear to have much shear strength properties which is exactly what the sprag clutch does to it. Shear it that is.
I use it on quite a few applications, just the plumbing supplies Polypipe SG100 which is easy to get.
Makes a really good seal on electrical plugs etc as it's virtually impervious to water.