First, and as an unrelated matter, I think I should be granted the title Advocatus Diaboli (Devil's Advocate) since I seem to be the one to question the validity of statements.
Second, on to the matter at hand, do we have any source for the claim "there are currently no human executions in the wizarding world?" I think that is very likely to be true, but it is a rather broad statement, and for every rule, there is usually an exception.
Finally, we do know that many of the Scourers in North America were executed. So this presumably required an executioner. "Those convicted of murder, of wizard-trafficking, torture and all other manners of cruelty were executed for their crimes." Wva (talk) 20:53, June 26, 2016 (UTC)