No, volunteers cannot edit the shifts they have signed up for, but you can set up a cancellation policy and allow them to cancel a registration. The advanced portal is required if you would like constituents to be able to cancel their own registrations.
These articles explain more about cancellation policies: https://support.donorview.com/en/support/solutions/articles/9000267268-cancelling-event-levels-and-add-ons
Internally, you can reassign someone to another recurring event's date or level using the transfer feature in the Tools menu.