You can fake a voice, (Actually I am assuming they are just going to be using sound clips so that is a mute point anyway.) you can not as easily fake a person's looks, especially in this case, unless you do black face which WOULD be offensive. Anyone remember how ridiculous white people looked trying to look Asian, either because there were no Asians around to play them or the director just did not want to use them. I am sure there may have been other reasons, the point is it was hard to watch. And I am not even going to get into the controversy with black face back in the day. Tom has to be darker than white. Not pitch black, but he has to resemble something other than white or Asian.
I just watched a video on YouTube of Tom teaching the Tornado Kick. Actually he is a lot "lighter" than I remember. But he is still darker than "white". Unless your cousin has a decent sun tan and then puts on the same clothes and wears dreads... I am not sure how realistic it will look. That is not to say it wont turn out alright. But putting so much effort into this with a passion as you have, I assume you want it as good as possible. Come to think of it, using a "black" person would actually not look like Tom either... and I have seen much darker Jamaicans...
I must have missed the picture... is it posted on here some where for easy viewing? I hate clicking on links myself. Maybe you can show us your cousin as he is now and then in costume and let us decide. For all we know he may already be the Tom you need and we are just over analyzing it.