Why does it require any shielding? Your detectors and coupler are already shielded. Are you concerned about the emissions off your digital stuff? If so, what is coming off that display?
Why? Best practices design if nothing else. It just makes sense to me to have this type of project in a shielded box. Doesn't it make basic design sense to you?
I mean, let's put it this way - if I didn't put this in a shielded enclosure, what do you think the peanut gallery would say to me? I'll tell you exactly what -"You should have put your project in a shielded box if it's sitting right next to high power radios". 
To me, it doesn't make much sense. All of your RF signals are already enclosed. If there was a concern about emissions, you may want to try and find a way to shield that gaping hole where the display is, not to mention the emissions from the display itself. If it is susceptibility of the little digital board, that may make more sense.
I would assume the high powered radios are radiating off the antenna which is not pointed back towards the lab. If they do produce a lot of emissions in the lab, maybe that should be addressed rather than trying to harden everything else.
From a professional work stand point, typically I will test my designs in the chamber with no shielding. If I can get them to pass there, typically going forward things are smooth sailing. Current career is pretty tame so not normally a big deal.
Now granted the nutter butter peanut butter crunches may look at all that waveguide frequency extender stuff I am playing with and suggest an enclosure would have greatly improved things. After all, that thing is a mess compared to what you are doing and working at much higher frequencies and fairly low noise. The only person I think that called it out wasn't suggesting the lack of a shielded case was the problem but rather the software.
https://www.eevblog.com/forum/rf-microwave/experimenting-with-waveguides-using-the-litevna/msg4797743/#msg4797743So, sure, it is now in a somewhat shielded box. Not for RF performance but instead, mechanical stability and size reduction.