When being first approached by a task (especially in a larger organisation), it's always a good idea to remain humble and ask yourself 'is there anyone else who can do this task better than I can?'.
If the answer is yes, then your response to a non-relevant task is:
The best person for that is (name here)
Or a non-relevant question:
The best person to ask about that is (name here)
This constructively does a number of things; firstly, it indicates you're not the best person to ask for this particular task (IE your specialism lies elsewhere), it lets them know who is, and it redirects their effort to achieving their outcome (don't offer to contact the person or they might see you as a helper of some sort they can just run to. Offer up the contact details or best direction, or if you don't know the contact details, point to someone in your immediate vicinity who you think does).
Naturally, some execs might not take the hint and might ask pointedly:
Why can't you do it?
Which is why it's important to have completed the first step (by determining the best person for the task you've also answered this question). I try to remain humble here and say:
(name) knows (way) more about (thing) than I do, and he's part of (department) who (specialise/deal with) (thing), I'm 'just' a(n) (role)
So, I'll get asked 'can you reprogramme the printer for me?', I might reply 'It might be best to ask one of the other staff members here, as I only deal with computers, and I rarely touch the printer.'
If you don't know anyone specific, you can just shrug your shoulders and say:
Sorry, I can't really help you with that, as I'm 'just' a(n) (your role). Maybe someone down in (role) department can help you with that?
The above worked for me very well. I'm one of those 'all-rounder' job type males where people automatically assume if you can do one or several things really well, you can do everything, and I've often been asked to do tasks out of my depth or not related to my particular area of expertise (I'm actually a programmer).
You don't usually explicitly tell anyone you're any specific thing, you just infer that there might be other people far better suited to their particular query. This way, it avoids offense (because you're actively appraising other staff members and seeing them on an equal footing).
If they absolutely insist (as some are wont to do), then defer them to your manager (if they aren't your manager) as they're the ones who have to approve your reassignment (as they manage your time):
You'll have to have a word with (name of manager) about me doing (task), as (I don't know what they have schelduled for me yet/they might have to fit it into the schedule).
By requiring the exec go through the hoops of due workplace process, the chance of them returning to you with 'just a small favour' will diminish, and the honest execs will know the best place to make a direct port of call.
If they ask you to do the task, ask them if they've spoken with your manager yet, and then confirm with your manager. If they haven't left the spot and are still asking, simply defer again and say:
I think (name of your manager) has a (big) project planned for me today, so I can't commit to it right now. If you speak with (him/her) about it, I'm sure they can sort something out.
For your present situation, as you've already accepted, just repurpose the above phrase:
You'll have to have a word with (name of manager) about me doing (task) on a regular basis, as (I don't know what they have schelduled for me yet/they might have to fit it into the schedule).
Be like Wally out of Dilbert: Defer, defer, defer!