This is a very good question.
My answer to this is, no, only the team members at the table may handle mission models.
If you want to continue reading, I'll start with some history and philosophy, and end with the rule citation.
Over the past five or six years, the rules about what team members away from the table may handle have varied. I am a big fan of allowing team members who are waiting to tag in also hold on to (and prepare) the robot attachments and strategic objects that they will be using, but there are plenty of people who think that this might lead to some nefarious practices (whatever those might be.) This year's rules don't explicitly talk about much about the difference between the team members at the table (often referred to as the "Robot Handlers") and the rest of the team members. Rule 2 says that there are two Robot Handlers, and that team members may tag in and out, but not much else about them.
The rules about Storage and Workspace (Rules 21, 22 and 28) allow stored objects to be handled and stored "by hand". There is no explicit wording that differentiates between the Robot Handlers and other team members. So I interpret this as allowing team members other than the Robot Handlers to hold on to attachments and strategic objects to ready them for use.
It's been a "generally accepted principle" (i.e it's not official for the Robot Game) that only the two Robot Handlers can manipulate things for strategic purposes. I agree with this principle. It levels the playing field a tiny bit between small teams and large teams. So how do I justify enforcing it?