i added an answer and then realized it was a complete nonsense, i was getting at the following question.

Suppose kappa is a regular cardinal and every set in H_kappa has a sharp. Are there transitive models of ZFC, M and N, such that

1. M and N have height kappa
2. for some stationary in kappa set S, for every alpha in S, both M and N compute alpha^+ correctly,
3. for some stationary set D, for every alpha in D, alpha is inaccessible in M
4. N has no inaccessible cardinals. 

i think the answer must be provably no.