"A knight had only to swop his armorial surcoat and shield for those of another to be safely taken for that person." (Hanley, Catherine., War and Combat (1150-1270): The Evidence from Old French Literature, p33)
A knight only had to put on someone else's cloths to be identified as that person.
I wonder where the exact problems are in your sentence. Maybe you can elaborate a bit more on the specific problems you face - or why you want it "simplified"?
Safely simply indicates that the knight does not risk to be found out.
We are talking about a time when people did not carry (photo) identification, and the only way - short from personally knowing the person - to identify someone was to ask their name.
For a knight, or for nobility, once heraldry became common, you could identify them by their (coat of) arms. This could be displayed on a seal, on a banner, or on their coat - the armorial surcoat. This coat or cape displayed the coat of arms or much simpler, the personal heraldic colours or shield of the wearer - or that of their lord.
So if a knight would put on a different knight's coat, he would become that other knight for all intents and purposes.
As an example, the Knights Templar wore a long white coat with a red cross on it. This was not just because it looked nice, it identified them as a Knight Templar. All someone had to do to be identified as one of them was simply take that coat and put it on. Of course, the actual owner of the said coat would very likely object to that.