@dabbadabba,
I think the first sentence is clearer.
The first sentence leaves open the possibility that you might finish Wednesday or Thursday, but are prepared to finish on Friday if it goes that long. Either way, it implies you will be done by the end of the week, unless something else is stated to change that.
When you specify that the action will continue through the
end of the week you are saying that for sure, you will still be working on Friday. Which brings up the possibility that you might need to go into the next week to finish.