I'd say those qualify as cheap solutions.
Most teams try internal option first. They're the easier ones to undo if the situation changes or something doesn't work out.
No one seems wild abut Hamilton, but so far, he really has not had much of a shot. His career consists of 98 innings in the field and 44 plate appearances. Scouting reports are not kind to his defense, but the Sox stayed with a few games of the wild card last year with Kike Hernandez completely butchering the position. Hamilton won't get a Gold Glove vote, but can he at least outplay Kike? And he's only in a part time role for now, probably at least until the sox know how long Story will be out. Even if that takes two weeks, will 8-12 games of Hamilton at SS completely derail this team this year?
I expect once they know what is going on with Story, this situation changes. Either with a new SS coming in, a movement of Rafaela to SS, or they try Vaughn Grissom there for a while. The last one is the most likely, since they need a place for him to play, he has played several full (minor league) seasons in that role, and he can hit, which Cora seems to prefer over defense-oriented players...