One can't assume that it would not have made any difference to the jury, just like I can't assume that it would.....The fact is they were not aware....and the other fact is that the outcome may have been different if they had known.

So.. scenario 1:
We had hand swabs tested and they showed only very low levels of lead, far lower than would be expected if she had loaded and fired the gun.
Or scenario 2:
We submitted the hand swabs and they were at first rejected because they could have been contaminated by other weapons, so we submitted them again and they showed only very low levels of lead, far lower than would be expected if she had loaded and fired the gun.
What difference does it make?
In any case, the court of appeal will decide firstly whether or not the new evidence renders the verdict unsafe and only if they can't make a decision on that will they ask whether or not it would have affected the decision of the jury. In the absence of any evidence of a conspiracy to submit falsified swabs the answer to both of those questions must be no.