Just for the record any prosecution has to jump a few hurdles first...
1) assuming you are a sensible otherwise law abiding person you have to have done something that alerts the plod to your carrying a knife or sharp implement in the first place; maybe it fell out of your pocket when paying for something at the supermarket and they call the cops or maybe you are trespassing and the landowner calls the cops; you get yourself stop searched or arrested then searched; they can do it either way ;-)
2) you rightly have the opportunity to explain yourself to the individual bobby, who may / or may not accept your version of events and let you go on your way; or arrest you; if they arrest you remain completely cooperative; violence or loud behaviour won't help your case;
3) you get interviewed at the police station. If you admit it you get charged to court. If you offer a defence the matter is reviewed by a cps lawyer who decides if you get charged to court; in my experience the cps will take a very practical view and err on the side of common sense;
4) if you do get charged at this stage you may well be on a sticky wicket but you still have the chance to present your defence to a magistrate who may also agree or not with your defence.
I could go on and there at least a thousand "but what if's" but rest assured the cops really do have better things to do than search people who are polite, cooperative and respectful. They really do prefer to target real crooks. The vast majority are entirely reasonable and if your reason to be carrying is sound (and current) then you really have little to fear.