Sadly, your instincts are absolutely right, brichi !

(So it's far from being a "dumb question"...)

The housing is configured as a metal shield,  for the precise purpose of ensuring that only RF coming from the antennae (hence primarily "pre-limited" to the band for which the antennae are tuned) reaches the sensitive input stages of the receiver.

It's my firm opinion that the above fact, along with the high volume of (relatively weak) broadband RF "junk" emitted by digital gear such as CD players, renders that particular relocation plan fraught with danger.

Accordingly, when space is tight, I tend to first consider a more "modular" approach that's based on cabling between individual separately housed components, (with only the "controller" needing to be directly in front of the operator) rather than all systems being "locked into" one all-containing "slab".