that is totally uncool...I think a totally unbiased party, or a proven honest one, should do the drawing either way because drawing out of a hat does not make it "safe" from the TD who "manages" the draw
best thing to do is call the manager, bartender, waitress, etc over to do the draw, AND the placement on the chart...if it is online they only need to push one button and it is done because a TD, or biased person drawing, can also "manage" things by who they pair and at what point on the chart