I've provided few variations on one basic concept. I tried to incorporate all three elements required by your brief: 1. Obvious briefcase frame element; 2. Cloud based/connected software, and 3. Agreement, or despute resolution between two sides.
Concept on entries #131 and #133, because of its simplicity is probably the best branding solution. It has basic briefcase element, cloud segment, as well as duality, subtly presented!
Concept on entries #128, #129 and #132, has all these elements, but also includes representation of your software, as a middle man/person, or mediator. This was additionaly emphasized by accent color! From branding point of view, this also might be good/recognizable visual identity!
Concept on my entries "130 and #135, involves paper files, as a symbol of agreement, packed in a briefcase, via cloud service!
Finaly, on my entry #126, there's most obvious representation with handshake, also including elements of cloud and briefcase. Handshake is something you've suggested, but this element might be overused on legal/business/corporate logos,...lack of uniqueness might be downside here!
Feel free to suggest improvements on any of these designs! Thank you!