Here's what I think:1.shake up - to disturb or rouse (people) so as to make them more energetic. Fine. Without 'up', it only means to move them physically, usually to wake them.
2. shake somebody up - to surprise somebody and make them think about something in a different way, become more active, etc. Shaken up by the early goal against them, the team began to fight back.
shake something up. Fine; possible without 'up'.
to make important changes in an organization, a profession, etc. in order to make it more efficient. The whole industry needs shaking up. Fine; not likely without 'up'
3.shake up; To upset by or as if by a physical jolt or shock: was badly shaken up by the accident. Fine. possible without 'up'
To subject to a drastic rearrangement or reorganization: new management bent on shaking up the company.That can be of help putting these skills into practice. Fine; not likely without 'up'
4. to stir the feelings of : upset, agitate <shook her up> Fine; OK without 'up'
5.To disturb or agitate; unnerve: She was shaken by the news of the disaster. Fine; OK with 'up'
[transitive] (not used in the progressive tenses) to shock or upset somebody very much
shake somebody He was badly shaken by the news of her death. Fine; OK with 'up'
shake somebody up The accident really shook her up. Fine; OK without 'up'