Caution: I AM NOT A LAWYER.
We recommend custom-made throwing knives which have no sharp edge, for throwing. In addition to being much safer for the thrower, this also means that the knife is more likely to be interpreted as for sport throwing, rather than for any nefarious intent.
When transporting knives and axes to and from a throwing venue, keep them in a case or bag, ideally one that is locked. Never wear your knives or axes while travelling to/from a venue.
Badges, logos, etc. of throwing groups on the bag/case and on your clothing will also help.
If practising away from a specific throwing venue, ensure that you are on private (not public) land, with permission from the owner, and make sure that you take steps to ensure that people are not going to accidentally wander into the area near or behind the target.
Ultimately, in the Scottish and English legal systems, much is down to the interpretation of the officers, prosecutors and judge involved. It is in your interests to be sensible in your conduct, and to act in a manner that makes it clear that you are in possession of knives and axes solely for the purpose of throwing, and to show concern for the safety of the general public around you.