Thanks for the question, it's an interesting one. In short, Henry had to order the swordsman before Anne's trial for Anne to be executed quickly. For the executioner to arrive on the 18th, the planned date of execution, he would have had to have been ordered by around the 12th or 13th and even as early as the 9th or 10th. He had to cross the channel and then make his way by horse from Dover to London. Weir is of the opinion that Cromwell wanted everything to move fast so that Henry didn't have the time to think about things and change his mind.
The fact that Henry ordered an expert French swordsman has been seen as an act of mercy because Anne could have been burned or beheaded in the usual way. Burning was an awful death as the victim could suffer quite a long time, particularly if the wood was damp. Beheading could also be a slow way to die if the axeman missed the neck and it took a few blows to finish you off. Death by sword, however, was very a very quick and clean death, so it could be seen that Henry was being merciful to Anne by letting her die in this manner.
However, the fact that the swordsman must have been ordered before Anne's trial even took place does call into question Henry's mercy and shows that Anne had been pre-judged as guilty and had no chance of being found innocent. Alison Weir points out that the ordering of the French swordsman before the trial shows that it had always been planned that Anne would die this way and that Henry actually showed cruelty in making Anne wait in suspense to find out how she would die. It is also likely that the promise of a more merciful death was used as a bargaining chip to get Anne to agree to the marriage annulment.
Anne's death by sword may also have been a political move. Anne was Queen and her execution was going to stir up a lot of controversy around Europe. If Henry could be seen to be acting in a merciful manner and giving her a dignified death then perhaps Europe would not be so horrified!