We live in the age of computers, allegedly paper is out, computers are in.
CAsA are environmental vandals. How many trees are used to produce the vast volumes of "shelf ware" required to be involved in aviation? Still even if everything was "computerised" you'd probably need a "Cray" computer to store it all in, but thats another story.
I've encountered several XL based computer programs that quickly check your CG
even flagging when an limit is breached. There are also facilities on some of the flight planning programs available that allow you to set up a quick and easy W&B check for your aircraft. I know there are a few FOI's with a 1950 mentality who will tell you these must be "Approved" i.e. pay us a bunch of money, then get a weight and balance delegate to put their signature on it so we are absolved of all responsibility and liability before you can use it, but I doubt they would have much success trying to make you into a criminal (felon. There goes any chance of an overseas holiday). CAsA may have no common sense when it comes to these things, but I imagine they would have a hard time convincing a court that the intent of the act has not been met.
FGD 135 is correct that a load sheet is not required, but a fairly simple way to get them off your back is Photocopy the trim sheet in A5, laminate it, and stick it in the roof lining or somewhere accessible. If in doubt about your CG its handy because you don't need to rifle through the FM to find a trim sheet, if you want real accuracy a china graph pencil is all you need. If an FOI asked for a trim sheet show them the card, as long as its got china graph smudges all over it to indicate its been used that should be sufficient to prove "Compliance".
I heard a story regarding one of those power mad FOI's at an event. The person he was harassing finally had enough and head butted him. By the time the coppers arrived all the witnesses had lost their memories.