Daleandrewswire,
I'm a pilot and mechanic (engineer), and an asthmatic. Throughout my career, I've done a lot of jobs, among them a number of years as a firefighter on the ground, and in flight. Asthma hasn't stood in my way. I am not familiar with regulation in your location, if it's outside the US, but asthma shouldn't prove a barrier to employment as a mechanic, at all.