That's probably too much railroading. The players will be able to sense that, especially after the encounter is over -- and they may feel shafted, etc.
It is more railroading than I'd prefer, but it is a required plot hook. Without it, the following adventure can not occur. If possible I'd like the encounter to feel 'fair' (i.e. the players might have been able to stop it), but it absolutely has to end with the above conditions met.
Moreover, your inital description of the "surprise round" doesn't hold water. All sides are aware of each other - regardless of apparent alliances - and so no surprise round is possible.
"The wizard and the duke walk up to the book. Standing over it, the wizard begins the incantation to safely remove it from its pedestal. Suddenly, he falls backwards, as if unconcious. As the duke steps forward to catch him, the wizard grabs the duke, lightning seething from his hands. Roll for initiative."
It makes perfect sense to me to let the wizard act before anyone else. What would the PC's do, if they beat the wizard on initiative for this first round, anyway? The wizard wouldn't have done anything at that point yet, so it would make no sense to move into a combat round.
If you want to be completely literal about it, then read the first line of "surprise" (PHB pg 137): "...if you are not aware of your opponents and they are aware of you, you're surprised". The PC's do not know the wizard is their opponent, until he attacks the duke. The wizard knows the duke is his opponent. Therefore, the wizard surprises the duke and the PC's.
If a PC had spellcraft skill, asked and succeeded in identifying the spell cast (shocking grasp), and decided something wasn't right, then I would allow them to go on the surprise round.
Since you want the duke dead, why not start the game off right there?
"You head into the tower with the duke, the wizard, and their bodyguards. The wizard picks up the book and laughs evilly, then spins around and casts a terrible spell on the duke! He screams in terror and falls to the ground, dead!
Roll for initiative..."
That is essentially what I'm planning. Surprise round -> wizard kills duke -> roll for initiative. I guess I should have made that more clear, that the duke won't really be fighting.
The only problem with the encounter that I see is that the PCs don't really have much to win. They can get out with their lives, but that still smells like defeat. It's more fun to start off with victory. I can't see how they can grab a victory out of this, other than killing the wizard, and you don't want that to happen.
1. you don't see this scenario as being about spotlighting the PCs.EVERY scenario should be about spotlighting the PCs. The don't need to be the extras watching your NPCs do things. That likely will be no fun for the players.
2. If "the duke dies" is the gotta happen part of the plan, then you need to give your players something other than "protect the duke" as their motivation for being there. Right now, they are being hired, and presumably this will be a "no choice" job, to go with the duke and keep him happy yet you are preordaining that they have to fail no matter what. Its almost always BAD to script mandatory regardless of choices FAILURE for your PCs.
The combo of 1 and 2 make the PCs meaningless to this series of events.
Let me try a different approach...
The encounter does spotlight the players, just not in terms of combat.
The wizard is framing the PC's for the murder of the duke, the guards, and himself. The entire adventure is about the PC's proving their innocence, while being fugatives from the law. This is how they get themselves into that situation. If the PC's weren't there, the wizard would have no one to frame for the murder; therefore, the PC's are a vital part of the plot. Later on they will get their revenge against the wizard, but that is a long ways away. This is just the start of the adventure/campaign.