I think this falls under the "shouldn't piss off real people with rules ambiguity/technicality" rule. I can read the rules going both ways (as evidenced by this thread).
You can read hold person's "cannot take any actions" as "you can't do anything that requires an action" meaning delay is fine or as "your only option is try to save" meaning delay is beyond you (it is a compulsion effect). You can also read delay as no action meaning that it doesn't cut into your action budget but is still an action (active answer to "it's your turn, what do you do?" in combat or you can read no-action as not taking any actions.
Personally I would rule in favor of not being able to delay. You're aware of what is going on but not able to react. Basically, you don't get a turn. You get a saving throw, which, if you succeed, gives you a turn with a full-round action missing from it.
Otherwise you open up a huge can of worms:
"You're panicked."
"I delay until it wears off."
Panicked says you can take no other actions but delay isn't an action. Only difference with Hold Person is that hold person says you do nothing rather than saying you run away (in before "but delay is nothing").
If you're waiting are you doing something?