I am trying to establish whether it is consistent that some property holds at the least weakly compact cardinal. I know that the property holds at measureables.

Hence (hoping everything else goes well), a natural approach would be to find some forcing extension in which the measurable cardinal becomes the least weakly compact.

Can this be done? Since a measurable cardinal has a cofinal sequence of weakly compact cardinals, if such a extension is possible, it would necessarily kill the measurability of the cardinal. A weaker question is if there there is a forcing extension where a measurable cardinal $\kappa$ in the ground model is not measurable but still weakly compact in the generic extension?

Are there forcing extensions that kills weakly compact cardinals? Given a positive solution to the weaker question above, perhaps applying the weakly compact killing extension to that extension, one may be able to make the cardinal the least weakly compact. Although there may be some trouble since in the first extension $\kappa$ may still be a limit of weakly compacts.

Thanks for any information that can be given.