I guess like all laws it depends on jurisdiction, and more importantly, if you can convince the judge/magistrate that the contract did or did not happen
Yeah, but the law still sets the default baseline for he judge / jury / whatever. In the Nordic countries (at least Sweden) -- as techno-modern and bureaucratic as they may be -- that still includes verbal agreements.
(The handshake is probably not a legal requirement, though I suppose it could be taken into consideration as evidence -- "You even shook hands on it, so you must have realised that what you had just discussed were atually the terms you were agreeing to.")