Frankly, I think it's physically impossible to copy anybody's sound.
The head, chest and hands of a player all form the resonating chamber for the harp. To get Sonny Boy or Little Walter's tone, your head, chest and hands all need to be identical to them, in addition to technique.
I believe that a complete different set of variables can lead to the same result. So, I believe that a player can sound like another player he wishes, even if the situation is completely different.
But I, personally, have not yet wished to sound exactly like someone else.
Regards,
Fernando