Different Timeline
Henry, Prince of Wales, was regarded with promise and his death from typhoid in 1612 was a huge blow to the Stuarts.
As stated, he would have become King on the assassination of his father in 1605. It's possible that his trusted Tutor, George Lauder, might have come to England to assist the young King.
On the assumption we can butterfly away the typhoid of 1612, Henry IX "could" have become a significant and positive king. It's entirely likely that the developments which would lead to the Civil War wouldn't occur under Henry but that's not to preclude the likelihood of growing tension between King and Parliament.
We might conjecture that a more efficient, effective and "popular" absolutism might be instigated by Henry in the 1620s though again it's hard to see how some form of conflict with the evolving middle-class wouldn't happen.
It's all conjecture but Henry's accession and reign would certainly reduce Charles Stuart to the sidelines of history.