This is probably doable. There are materials I have used in the past that are extremely lightweight that can be used to shield the CB. It is common practice to use aluminized or coppered mylar as shielding for hi speed data transmission cables for example. Would save at least 25% of the module's weight but would require someone with an O-Scope to do the necessary experimentation.

Some form of covering is necessary to shield the radio from the module's radio frequency intereference emissions.

BTW- with JR radios (2.4 gig) that use satellite Rxs, it's a good idea not to get any satellite within 6" of the module. More distance is better