To that end, he will weigh his options and decide on a particular team that has cap space. The team has to have cap space or Bosh has no leverage to go to the Raps. At that point, faced with losing Bosh to that team no matter what, they might as well get some minor piece or picks back.
These people take their money very seriously, Bosh is not going to make a list of teams he wouldn't mind going to as another poster put it. He will bring to the Raps the team he is for sure going to even if the Raps don't sign him before. That way he has security in his new team and leverage over the Raps.
Bosh is looking for what's best for him, cap space or not.
As such, I disagree with your assumption that Bosh will decide on a particular team that has cap space. Bottom line is there may be more attractive locations with teams that don't have cap space. In other words, if LA or Houston is number one on his list, and Colangelo can work out a deal, then he'll likely go there instead of a team with cap space.
The key in whole equation is how many teams is Bosh interested in joining. If his heart is set on the Knicks than we'll be lucky to get .75 cents on the dollar. However, if he has two or three teams that really interest him, the chance of a better return increases.
But don't rule out the teams without cap room. That just doesn't make any sense at all.