Is it permitted to delay your turn when you're an unsurprised combattant in the surprise round?
There is nothing to prevent this in the surprise or delay rules. Delaying is a free action, which you can take during a surprise round with one exception (you can't use an action point during a surprise round).
The only consequence here is that you end up in a later spot in the initiative order.
You can also ready an action during a surprise round, as you are allowed to both take a standard action (the action type for ready), and an immediate actions (which is the type of action the trigger is).