My understanding of your question is that you want to:
- Use the Ready Action (there is no "Hold" action) to cast Booming Blade with a trigger of "when that guy acts".
- Having cast a cantrip, use the Illusionist's Bracers and your Bonus Action to cast Booming Blade and immediately attack "that guy", applying Sneak Attack if you hit.
- "When that guy acts", use the trigger to make the original Booming Blade attack, applying Sneak Attack if you hit.
The rules casting using the Ready Action are:
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs.
So, on your turn, you have cast a cantrip. Per the Illusionist's Bracers "whenever you cast a cantrip, you can use a bonus action on the same turn to cast that cantrip a second time." So you can do that.
As per the errata, you must use a weapon as a material component to cast the spell and must use that weapon to make the subsequent attack, which is not part of the casting, it is part of the effect.
The Ready Action Booming Blade attack and the Bonus Action Booming Blade attack occur on different turns so they are each eligible for Sneak Attack which can be used "once per turn".