Mulligans
General Mulligans
Use your Ursatron's with Fireworks Tech, Nine Lives etc. to draw both your Galvanizer's and Mecha'thun. Use Goblin Prank on your 8 cost Mecha'thun so it dies after your deck and hand is empty. Dont just throw Ursatron out without a way to trigger his deathrattle a few more times. Card draw is tricky so use your card draw cards wisely.
Aggro Mulligans
You're going to want minions, card draw, and your board clearing spells to live against aggro. Card draw may be the downfall here.