Can I schedule Apple Watch delivery to a pickup point, or select a time to suit me?

Only by making post-shipping delivery arrangements with the shipping company.

Usually, they are quite helpful.

Depends on the actual shipping company. Apple generally uses - at least for its NYC deliveries - both UPS and FEDEX. Fedex will allow you to call BEFORE the delivery to ask for them to hold at their local facility. UPS makes you wait to miss the first delivery attempt and THEN you can call and ask them to hold it for pickup. Don't think either will give you the option of either changing the place of delivery or will actually schedule a time (not sure about the delivery time business).

Fedex though will give the option of having it delivered and held at one of the Fedex Stores, if their local delivery depot is not convenient.

With UPS you can request a change before the package is at the local depot and before it's put on a truck. You need to make a direct call for help. I've done this in the past. UPS has been helpful. It helps to call them as soon as you get the shipping notice with the tracking number.

WWell then you have had more success with UPS than I have because I was always told I had to wait for the first attempt.

Apple in the UK usually use UPS ( assuming you are in the original High Wycombe )😉 for shipments from European Distribution Centre in Ireland