I'd go with 1 if you have any indication that this will be accepted by the chair of the outreach committee. If you aren't reasonably certain of that, then I'd pass the buck up to the head of the CS department, whom I assume is nominally "your boss" (are you still a part time RA/part time PUOS person or did you get transferred to some other kind of contract?). Passing it up to your boss runs the risk that they might then come back and ask (tell) you to do it, but at least then it's coming from someone who nominally has some authority to allocate work to you. The HoD has more authority in re-assigning the work to the CS Dept Outreach officer.

Depending on your relationship with the HoD, and their preferred style of communications, I'd do this by email or by arranging to see them.