I lol'd at this question ... it is a good question though.
It is counter-intuitive to sterilize the needle, but what if at the last second the convict received a stay of execution, then got a nasty disease from the almost kill him needle. You know there be a lawsuit. What if one of the medical professionals accidently nicked themselves or such. Maybe the non sterilized needle had something in it that prevented the chemicals from doing their job properly or caused a botch execution.
Ultimately it is easier and safer for everyone if sterilized needles are used.