Yes, a Saveaway will do that. I
think the only way to get a non-Walrus one now is a Northern ticket office.
Yes, only thing is you can't do a full round trip in one go, you must break your journey and wait for the next ferry. This is what they mean by "can't be used on river cruises".
The ticket carries a "not before 9:30am" restriction on all modes - ferry, train and bus, except at weekends and Bank Holidays. You can use it until 6:29am but there won't be a lot running then!
Full validity information:
https://www.merseytravel.gov.uk/tickets/compare-tickets/pages/saveaway.aspx
It is valid on any TOC which has two station stops within the area of validity, which basically means
Merseyrail Electrics, Northern, LNR (WMT) and TPE. If you don't need that validity you can get the Merseyrail Electrics day ticket which is about 10p cheaper. The advantage of that ticket is that it is never issued on Walrus.