Yes — if your Google account has edit access to a shared calendar, WipeAway can clean it. All sharing permissions remain intact after the deletion.
Shared calendars appear in WipeAway's calendar list alongside your personal calendars, as long as the account you signed in with has edit (not just view) access to them. You can select shared calendars and clean them exactly as you would your own.
After the deletion, every person who had access to the shared calendar still has the same access. The events are gone, but the calendar setup is unchanged.
When you remove events from a shared calendar, those events disappear for everyone who has access — not just you. Let the other people who use the calendar know before you run a deletion, so they can note anything they need before it is cleared.
See also: Why can't I select a shared calendar? — if a shared calendar appears as "View only", you need edit access before WipeAway can clean it.