There is a fun amount of subterfuge in this backing and forthing.
First, these sailors aren’t so sure this is Horatio. But even so, they are charged with a) bringing Horatio a letter from Hamlet and b) bringing Horatio to Hamlet – after this negotiation with the letter. It’s like. Why did he need the letter? Couldn’t the sailors have said: “Horatio, Hamlet asked us to bring you to him. Come with us.”
But no. We have to have this letter in between – and it serves to create an atmosphere of espionage. It helps turn a revenge drama into a Spy Thriller.