I’ve done it all, on the CXer and in an afternoon..
It’s really easy, you can’t get lost on it but I’d advise you take an OS map or GPS with the route on. Only one “difficult” bit on the whole route and it’s only because it’s not marked, and that’s the section near Liss Forest where tracks criss cross the open moorland. Some lovely views, forgotten lanes and tracks that are well hidden from anyone. Lovely section down the old railway line which runs along a brook, it’s worth stopping off to spot the sculptures that mark the route too.
Lovely day out, not sure about 2 days but I guess if you take it really leisurely it’ll be a nice pootle.
Can’t help with accom but you do go through some small villages, maybe lucky in one of them.
Here’s the Hants.Gov site incl map and GPX file.
Hants Gov, Shipwrights Way