Can't comment on what the CAA would say but i'm sure they'll be, or have been along for a ride with your company at some point assuming it's UK registered etc etc.
From the airline perspective we tend to carry two sets of all approach plates en-route charts and supplements. Even my previous company flying TP's where space was at a premium we carried two sets (although limited to UK and near continent airfields).
At present my current company (UK Charter) has two each binders with 'everyday' airfields in and another three or four each with the others stored aft of each pilot along with all the other charts and books packed in with them.
I can perfectly understand that space is at a premium on many biz a/c and some of my collegues coming from the corporate world had similar issues.
My personal approach
would be to brief with the chart held between you and then set the aids/fmc up as you go or just after briefing if possible. Certainly if you are to be PF then it seems logical for you to have the chart on your side for quick reference and hand it over if required. I reckon you, as PF will be needing reference to it more than PNF, this is in an ideal world with an ideal world ILS.
On a non precision approach I think I personally would keep the chart my side for descent/approach planning/set up and then swap before getting to a critical phase i.e. altitude/height checks and calls. During a go-around i'm sure your collegue can assist in navigating the a/c around the hoops.
CRM is an easy answer but many you fly with may not demonstrate or think they require such training. It does seem a little unusual (from an airline point of view) to rely on memory for setting up aids and minima etc especially for unfamilliar airfields, but a lot of the info can be put into the FMC or noted down somewhere if the company insists on this way of briefing.
On a short sector and me PF i'd keep the plate as long as practical and you can better monitor what's being done etc. Or get them to fit dual EFB's
Interesting to hear others views....
Hope this helps
PP