If you put the objects on their own layer, you can click on the flyout menu on the layers window and choose Options for that layer. Then uncheck the Printing box. Just make sure you don't flatten the thing so you maintain that functionality.
For the above, It's often easier to just duplicate the layer with everything on it and select the objects you DON"T want - in this case, objects that you want to print - and then delete them. That saves any repositioning.
I still use AI CS. If you use a newer version, check the Attributes window and see if there's anything about non printing. Indesign has this and I don't know if Adobe maybe added it to AI.
Using OSX 10.3.9 on a G4