Law enforcement watches the mempool, they can spot such transactions anyway because they know it didn't ever show up in their mempool logs.
Little tiny 'gotchas' aren't going to save you from a determined investigator. They are trying to follow a trail of evidence so they can produce more evidence. What you need is a clean break, so that the investigator hits a dead end and has no productive leads they can follow.
Just pretend you sent that transaction a millisecond before it was mined.