Not going to happen. If Sigimund III is raised Protestant, then his uncle will have a harder time deposing him. However, the large majority of the nobility who voted in the Sjem for the King was Catholic, with Protestants maybe making up a 1/10-1/5 of the total (most of them being Lithuanians, who did not always even show up to vote).
The only way a Protestant Sigismund becomes King of the Commonwealth would be for him to conquer it in front of a Swedish Army, he would never be freely elected to the position unless he renounced his Catholic faith.